Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ -4{x}^{(2 + 12{x}^{(2ln(x))})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -4{x}^{(12{x}^{(2ln(x))} + 2)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -4{x}^{(12{x}^{(2ln(x))} + 2)}\right)}{dx}\\=&-4({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))\\=&\frac{-192{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x} - \frac{48{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x} - \frac{8{x}^{(12{x}^{(2ln(x))} + 2)}}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-192{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x} - \frac{48{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x} - \frac{8{x}^{(12{x}^{(2ln(x))} + 2)}}{x}\right)}{dx}\\=&\frac{-192*-{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{2}} - \frac{192({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x} - \frac{192{x}^{(2ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{2}(x)}{x} - \frac{192{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*2ln(x)}{x(x)} - \frac{48*-{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}} - \frac{48({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}}{x} - \frac{48{x}^{(2ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))}{x} - \frac{8*-{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}} - \frac{8({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))}{x}\\=&\frac{-192{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{2}} - \frac{768{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{2}} - \frac{9216{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{2}} - \frac{4608{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{2}} - \frac{576{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{2}} - \frac{384{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{2}(x)}{x^{2}} - \frac{576{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}} - \frac{48{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}} - \frac{96{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}}{x^{2}} - \frac{8{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-192{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{2}} - \frac{768{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{2}} - \frac{9216{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{2}} - \frac{4608{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{2}} - \frac{576{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{2}} - \frac{384{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{2}(x)}{x^{2}} - \frac{576{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}} - \frac{48{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}} - \frac{96{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}}{x^{2}} - \frac{8{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}}\right)}{dx}\\=&\frac{-192*-2{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{192({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{2}} - \frac{192{x}^{(2ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{2}(x)}{x^{2}} - \frac{192{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*2ln(x)}{x^{2}(x)} - \frac{768*-2{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{3}} - \frac{768({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{2}} - \frac{768{x}^{(2ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{3}(x)}{x^{2}} - \frac{768{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*3ln^{2}(x)}{x^{2}(x)} - \frac{9216*-2{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{3}} - \frac{9216({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{2}} - \frac{9216{x}^{(4ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{4}(x)}{x^{2}} - \frac{9216{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*4ln^{3}(x)}{x^{2}(x)} - \frac{4608*-2{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{4608({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{2}} - \frac{4608{x}^{(4ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{2}(x)}{x^{2}} - \frac{4608{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*2ln(x)}{x^{2}(x)} - \frac{576*-2{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{3}} - \frac{576({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{2}} - \frac{576{x}^{(2ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln(x)}{x^{2}} - \frac{576{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}(x)} - \frac{384*-2{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{2}(x)}{x^{3}} - \frac{384({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)})){x}^{(2ln(x))}ln^{2}(x)}{x^{2}} - \frac{384{x}^{(12{x}^{(2ln(x))} + 2)}({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)}))ln^{2}(x)}{x^{2}} - \frac{384{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}*2ln(x)}{x^{2}(x)} - \frac{576*-2{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}} - \frac{576({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}} - \frac{576{x}^{(4ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))}{x^{2}} - \frac{48*-2{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}} - \frac{48({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}}{x^{2}} - \frac{48{x}^{(2ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))}{x^{2}} - \frac{96*-2{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}}{x^{3}} - \frac{96({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)})){x}^{(2ln(x))}}{x^{2}} - \frac{96{x}^{(12{x}^{(2ln(x))} + 2)}({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)}))}{x^{2}} - \frac{8*-2{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}} - \frac{8({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))}{x^{2}}\\=&\frac{-4608{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{768{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{3}} - \frac{9216{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{3}} - \frac{110592{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{5}(x)}{x^{3}} + \frac{192{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{3}} - \frac{3072{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{3}} - \frac{442368{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{6}(x)}{x^{3}} - \frac{331776{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{3}} - \frac{110592{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{3}} - \frac{18432{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}ln^{4}(x)}{x^{3}} - \frac{4608{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{82944{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{9216{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}ln^{2}(x)}{x^{3}} - \frac{20736{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{3}} - \frac{1920{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln(x)}{x^{3}} - \frac{384{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{2}(x)}{x^{3}} - \frac{1536{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{3}(x)}{x^{3}} - \frac{576{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}} - \frac{6912{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}} - \frac{672{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}}{x^{3}} - \frac{1152{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-4608{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{768{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{3}} - \frac{9216{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{3}} - \frac{110592{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{5}(x)}{x^{3}} + \frac{192{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{3}} - \frac{3072{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{3}} - \frac{442368{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{6}(x)}{x^{3}} - \frac{331776{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{3}} - \frac{110592{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{3}} - \frac{18432{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}ln^{4}(x)}{x^{3}} - \frac{4608{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{82944{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{9216{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}ln^{2}(x)}{x^{3}} - \frac{20736{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{3}} - \frac{1920{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln(x)}{x^{3}} - \frac{384{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{2}(x)}{x^{3}} - \frac{1536{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{3}(x)}{x^{3}} - \frac{576{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}} - \frac{6912{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}} - \frac{672{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}}{x^{3}} - \frac{1152{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}}{x^{3}}\right)}{dx}\\=&\frac{-4608*-3{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{4}} - \frac{4608({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{4608{x}^{(2ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{2}(x)}{x^{3}} - \frac{4608{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*2ln(x)}{x^{3}(x)} - \frac{768*-3{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{4}} - \frac{768({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{3}} - \frac{768{x}^{(2ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{3}(x)}{x^{3}} - \frac{768{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*3ln^{2}(x)}{x^{3}(x)} - \frac{9216*-3{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{4}} - \frac{9216({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{3}} - \frac{9216{x}^{(4ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{4}(x)}{x^{3}} - \frac{9216{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*4ln^{3}(x)}{x^{3}(x)} - \frac{110592*-3{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{5}(x)}{x^{4}} - \frac{110592({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{5}(x)}{x^{3}} - \frac{110592{x}^{(4ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{5}(x)}{x^{3}} - \frac{110592{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*5ln^{4}(x)}{x^{3}(x)} + \frac{192*-3{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{4}} + \frac{192({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{3}} + \frac{192{x}^{(2ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln(x)}{x^{3}} + \frac{192{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}(x)} - \frac{3072*-3{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{4}} - \frac{3072({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{3}} - \frac{3072{x}^{(2ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{4}(x)}{x^{3}} - \frac{3072{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*4ln^{3}(x)}{x^{3}(x)} - \frac{442368*-3{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{6}(x)}{x^{4}} - \frac{442368({x}^{(6ln(x))}((\frac{6}{(x)})ln(x) + \frac{(6ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{6}(x)}{x^{3}} - \frac{442368{x}^{(6ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{6}(x)}{x^{3}} - \frac{442368{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*6ln^{5}(x)}{x^{3}(x)} - \frac{331776*-3{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{4}} - \frac{331776({x}^{(6ln(x))}((\frac{6}{(x)})ln(x) + \frac{(6ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{3}} - \frac{331776{x}^{(6ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{4}(x)}{x^{3}} - \frac{331776{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*4ln^{3}(x)}{x^{3}(x)} - \frac{110592*-3{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{4}} - \frac{110592({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{3}} - \frac{110592{x}^{(4ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{3}(x)}{x^{3}} - \frac{110592{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*3ln^{2}(x)}{x^{3}(x)} - \frac{18432*-3{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}ln^{4}(x)}{x^{4}} - \frac{18432({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)})){x}^{(4ln(x))}ln^{4}(x)}{x^{3}} - \frac{18432{x}^{(12{x}^{(2ln(x))} + 2)}({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)}))ln^{4}(x)}{x^{3}} - \frac{18432{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}*4ln^{3}(x)}{x^{3}(x)} - \frac{4608*-3{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{4}} - \frac{4608({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{4608{x}^{(4ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{2}(x)}{x^{3}} - \frac{4608{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*2ln(x)}{x^{3}(x)} - \frac{82944*-3{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{4}} - \frac{82944({x}^{(6ln(x))}((\frac{6}{(x)})ln(x) + \frac{(6ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{3}} - \frac{82944{x}^{(6ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln^{2}(x)}{x^{3}} - \frac{82944{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}*2ln(x)}{x^{3}(x)} - \frac{9216*-3{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}ln^{2}(x)}{x^{4}} - \frac{9216({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)})){x}^{(4ln(x))}ln^{2}(x)}{x^{3}} - \frac{9216{x}^{(12{x}^{(2ln(x))} + 2)}({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)}))ln^{2}(x)}{x^{3}} - \frac{9216{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}*2ln(x)}{x^{3}(x)} - \frac{20736*-3{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{4}} - \frac{20736({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{3}} - \frac{20736{x}^{(4ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))ln(x)}{x^{3}} - \frac{20736{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}(x)} - \frac{1920*-3{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln(x)}{x^{4}} - \frac{1920({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)})){x}^{(2ln(x))}ln(x)}{x^{3}} - \frac{1920{x}^{(12{x}^{(2ln(x))} + 2)}({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)}))ln(x)}{x^{3}} - \frac{1920{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}}{x^{3}(x)} - \frac{384*-3{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{2}(x)}{x^{4}} - \frac{384({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)})){x}^{(2ln(x))}ln^{2}(x)}{x^{3}} - \frac{384{x}^{(12{x}^{(2ln(x))} + 2)}({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)}))ln^{2}(x)}{x^{3}} - \frac{384{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}*2ln(x)}{x^{3}(x)} - \frac{1536*-3{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{3}(x)}{x^{4}} - \frac{1536({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)})){x}^{(2ln(x))}ln^{3}(x)}{x^{3}} - \frac{1536{x}^{(12{x}^{(2ln(x))} + 2)}({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)}))ln^{3}(x)}{x^{3}} - \frac{1536{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}*3ln^{2}(x)}{x^{3}(x)} - \frac{576*-3{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{4}} - \frac{576({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}} - \frac{576{x}^{(4ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))}{x^{3}} - \frac{6912*-3{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{4}} - \frac{6912({x}^{(6ln(x))}((\frac{6}{(x)})ln(x) + \frac{(6ln(x))(1)}{(x)})){x}^{(12{x}^{(2ln(x))} + 2)}}{x^{3}} - \frac{6912{x}^{(6ln(x))}({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)}))}{x^{3}} - \frac{672*-3{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}}{x^{4}} - \frac{672({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)})){x}^{(2ln(x))}}{x^{3}} - \frac{672{x}^{(12{x}^{(2ln(x))} + 2)}({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)}))}{x^{3}} - \frac{1152*-3{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}}{x^{4}} - \frac{1152({x}^{(12{x}^{(2ln(x))} + 2)}((12({x}^{(2ln(x))}((\frac{2}{(x)})ln(x) + \frac{(2ln(x))(1)}{(x)})) + 0)ln(x) + \frac{(12{x}^{(2ln(x))} + 2)(1)}{(x)})){x}^{(4ln(x))}}{x^{3}} - \frac{1152{x}^{(12{x}^{(2ln(x))} + 2)}({x}^{(4ln(x))}((\frac{4}{(x)})ln(x) + \frac{(4ln(x))(1)}{(x)}))}{x^{3}}\\=&\frac{4608{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{4}} - \frac{29952{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{4}} - \frac{1686528{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{4}} - \frac{13440{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{2}(x)}{x^{4}} - \frac{12480{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{4}} - \frac{10616832{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{7}(x)}{x^{4}} + \frac{73728{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{4}} - \frac{1032192{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{6}(x)}{x^{4}} - \frac{221184{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}ln^{5}(x)}{x^{4}} - \frac{21233664{x}^{(8ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{8}(x)}{x^{4}} - \frac{21233664{x}^{(8ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{6}(x)}{x^{4}} + \frac{1536{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln(x)}{x^{4}} - \frac{12288{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{5}(x)}{x^{4}} - \frac{13271040{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{5}(x)}{x^{4}} - \frac{6144{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}ln^{4}(x)}{x^{4}} - \frac{7962624{x}^{(8ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{4}(x)}{x^{4}} - \frac{884736{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(6ln(x))}ln^{6}(x)}{x^{4}} - \frac{4644864{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{3}(x)}{x^{4}} - \frac{663552{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(6ln(x))}ln^{4}(x)}{x^{4}} - \frac{576000{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{4}} - \frac{1327104{x}^{(8ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln^{2}(x)}{x^{4}} - \frac{294912{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}ln^{3}(x)}{x^{4}} + \frac{18432{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{4}} - \frac{497664{x}^{(6ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}ln(x)}{x^{4}} - \frac{165888{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(6ln(x))}ln^{2}(x)}{x^{4}} - \frac{59904{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}ln(x)}{x^{4}} - \frac{1920{x}^{(2ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{4}} - \frac{20736{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(4ln(x))}}{x^{4}} + \frac{864{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(2ln(x))}}{x^{4}} - \frac{6336{x}^{(4ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{4}} - \frac{82944{x}^{(8ln(x))}{x}^{(12{x}^{(2ln(x))} + 2)}}{x^{4}} - \frac{13824{x}^{(12{x}^{(2ln(x))} + 2)}{x}^{(6ln(x))}}{x^{4}}\\ \end{split}\end{equation} \]