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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 4cos(2)x{e}^{x}tan(x){sin(x)}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 4x{e}^{x}sin^{2}(x)cos(2)tan(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 4x{e}^{x}sin^{2}(x)cos(2)tan(x)\right)}{dx}\\=&4{e}^{x}sin^{2}(x)cos(2)tan(x) + 4x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan(x) + 4x{e}^{x}*2sin(x)cos(x)cos(2)tan(x) + 4x{e}^{x}sin^{2}(x)*-sin(2)*0tan(x) + 4x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)(1)\\=&4{e}^{x}sin^{2}(x)cos(2)tan(x) + 4x{e}^{x}sin^{2}(x)cos(2)tan(x) + 8x{e}^{x}sin(x)cos(x)cos(2)tan(x) + 4x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 4{e}^{x}sin^{2}(x)cos(2)tan(x) + 4x{e}^{x}sin^{2}(x)cos(2)tan(x) + 8x{e}^{x}sin(x)cos(x)cos(2)tan(x) + 4x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)\right)}{dx}\\=&4({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan(x) + 4{e}^{x}*2sin(x)cos(x)cos(2)tan(x) + 4{e}^{x}sin^{2}(x)*-sin(2)*0tan(x) + 4{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)(1) + 4{e}^{x}sin^{2}(x)cos(2)tan(x) + 4x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan(x) + 4x{e}^{x}*2sin(x)cos(x)cos(2)tan(x) + 4x{e}^{x}sin^{2}(x)*-sin(2)*0tan(x) + 4x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)(1) + 8{e}^{x}sin(x)cos(x)cos(2)tan(x) + 8x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(x)cos(2)tan(x) + 8x{e}^{x}cos(x)cos(x)cos(2)tan(x) + 8x{e}^{x}sin(x)*-sin(x)cos(2)tan(x) + 8x{e}^{x}sin(x)cos(x)*-sin(2)*0tan(x) + 8x{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x)(1) + 4{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 4x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)sec^{2}(x) + 4x{e}^{x}*2sin(x)cos(x)cos(2)sec^{2}(x) + 4x{e}^{x}sin^{2}(x)*-sin(2)*0sec^{2}(x) + 4x{e}^{x}sin^{2}(x)cos(2)*2sec^{2}(x)tan(x)\\=&8{e}^{x}sin^{2}(x)cos(2)tan(x) + 16{e}^{x}sin(x)cos(x)cos(2)tan(x) + 8{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 8x{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 16x{e}^{x}sin(x)cos(x)cos(2)tan(x) + 8x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 8x{e}^{x}cos^{2}(x)cos(2)tan(x) - 4x{e}^{x}sin^{2}(x)cos(2)tan(x) + 8x{e}^{x}sin(x)cos(2)cos(x)sec^{2}(x) + 8x{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 8{e}^{x}sin^{2}(x)cos(2)tan(x) + 16{e}^{x}sin(x)cos(x)cos(2)tan(x) + 8{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 8x{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 16x{e}^{x}sin(x)cos(x)cos(2)tan(x) + 8x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 8x{e}^{x}cos^{2}(x)cos(2)tan(x) - 4x{e}^{x}sin^{2}(x)cos(2)tan(x) + 8x{e}^{x}sin(x)cos(2)cos(x)sec^{2}(x) + 8x{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x)\right)}{dx}\\=&8({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan(x) + 8{e}^{x}*2sin(x)cos(x)cos(2)tan(x) + 8{e}^{x}sin^{2}(x)*-sin(2)*0tan(x) + 8{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)(1) + 16({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(x)cos(2)tan(x) + 16{e}^{x}cos(x)cos(x)cos(2)tan(x) + 16{e}^{x}sin(x)*-sin(x)cos(2)tan(x) + 16{e}^{x}sin(x)cos(x)*-sin(2)*0tan(x) + 16{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x)(1) + 8({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)sec^{2}(x) + 8{e}^{x}*2sin(x)cos(x)cos(2)sec^{2}(x) + 8{e}^{x}sin^{2}(x)*-sin(2)*0sec^{2}(x) + 8{e}^{x}sin^{2}(x)cos(2)*2sec^{2}(x)tan(x) + 8{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 8x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 8x{e}^{x}*2sin(x)cos(x)cos(2)tan(x)sec^{2}(x) + 8x{e}^{x}sin^{2}(x)*-sin(2)*0tan(x)sec^{2}(x) + 8x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)(1)sec^{2}(x) + 8x{e}^{x}sin^{2}(x)cos(2)tan(x)*2sec^{2}(x)tan(x) + 16{e}^{x}sin(x)cos(x)cos(2)tan(x) + 16x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(x)cos(2)tan(x) + 16x{e}^{x}cos(x)cos(x)cos(2)tan(x) + 16x{e}^{x}sin(x)*-sin(x)cos(2)tan(x) + 16x{e}^{x}sin(x)cos(x)*-sin(2)*0tan(x) + 16x{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x)(1) + 8{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 8x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)sec^{2}(x) + 8x{e}^{x}*2sin(x)cos(x)cos(2)sec^{2}(x) + 8x{e}^{x}sin^{2}(x)*-sin(2)*0sec^{2}(x) + 8x{e}^{x}sin^{2}(x)cos(2)*2sec^{2}(x)tan(x) + 8{e}^{x}cos^{2}(x)cos(2)tan(x) + 8x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos^{2}(x)cos(2)tan(x) + 8x{e}^{x}*-2cos(x)sin(x)cos(2)tan(x) + 8x{e}^{x}cos^{2}(x)*-sin(2)*0tan(x) + 8x{e}^{x}cos^{2}(x)cos(2)sec^{2}(x)(1) - 4{e}^{x}sin^{2}(x)cos(2)tan(x) - 4x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan(x) - 4x{e}^{x}*2sin(x)cos(x)cos(2)tan(x) - 4x{e}^{x}sin^{2}(x)*-sin(2)*0tan(x) - 4x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)(1) + 8{e}^{x}sin(x)cos(2)cos(x)sec^{2}(x) + 8x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(2)cos(x)sec^{2}(x) + 8x{e}^{x}cos(x)cos(2)cos(x)sec^{2}(x) + 8x{e}^{x}sin(x)*-sin(2)*0cos(x)sec^{2}(x) + 8x{e}^{x}sin(x)cos(2)*-sin(x)sec^{2}(x) + 8x{e}^{x}sin(x)cos(2)cos(x)*2sec^{2}(x)tan(x) + 8{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x) + 8x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(x)cos(2)sec^{2}(x) + 8x{e}^{x}cos(x)cos(x)cos(2)sec^{2}(x) + 8x{e}^{x}sin(x)*-sin(x)cos(2)sec^{2}(x) + 8x{e}^{x}sin(x)cos(x)*-sin(2)*0sec^{2}(x) + 8x{e}^{x}sin(x)cos(x)cos(2)*2sec^{2}(x)tan(x)\\=&24{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 48{e}^{x}sin(x)cos(x)cos(2)tan(x) + 24{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 24{e}^{x}cos^{2}(x)cos(2)tan(x) - 12{e}^{x}sin^{2}(x)cos(2)tan(x) + 24{e}^{x}sin(x)cos(2)cos(x)sec^{2}(x) + 24{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x) + 24x{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 32x{e}^{x}sin(x)cos(x)cos(2)tan(x)sec^{2}(x) + 8x{e}^{x}sin^{2}(x)cos(2)sec^{4}(x) + 16x{e}^{x}sin^{2}(x)cos(2)tan^{2}(x)sec^{2}(x) + 16x{e}^{x}sin(x)cos(2)cos(x)tan(x)sec^{2}(x) + 24x{e}^{x}cos^{2}(x)cos(2)tan(x) + 24x{e}^{x}sin(x)cos(2)cos(x)sec^{2}(x) - 12x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 24x{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x) - 20x{e}^{x}sin^{2}(x)cos(2)tan(x) - 8x{e}^{x}sin(x)cos(x)cos(2)tan(x) + 8x{e}^{x}cos(2)cos^{2}(x)sec^{2}(x) + 16x{e}^{x}cos^{2}(x)cos(2)sec^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 24{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 48{e}^{x}sin(x)cos(x)cos(2)tan(x) + 24{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 24{e}^{x}cos^{2}(x)cos(2)tan(x) - 12{e}^{x}sin^{2}(x)cos(2)tan(x) + 24{e}^{x}sin(x)cos(2)cos(x)sec^{2}(x) + 24{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x) + 24x{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 32x{e}^{x}sin(x)cos(x)cos(2)tan(x)sec^{2}(x) + 8x{e}^{x}sin^{2}(x)cos(2)sec^{4}(x) + 16x{e}^{x}sin^{2}(x)cos(2)tan^{2}(x)sec^{2}(x) + 16x{e}^{x}sin(x)cos(2)cos(x)tan(x)sec^{2}(x) + 24x{e}^{x}cos^{2}(x)cos(2)tan(x) + 24x{e}^{x}sin(x)cos(2)cos(x)sec^{2}(x) - 12x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 24x{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x) - 20x{e}^{x}sin^{2}(x)cos(2)tan(x) - 8x{e}^{x}sin(x)cos(x)cos(2)tan(x) + 8x{e}^{x}cos(2)cos^{2}(x)sec^{2}(x) + 16x{e}^{x}cos^{2}(x)cos(2)sec^{2}(x)\right)}{dx}\\=&24({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 24{e}^{x}*2sin(x)cos(x)cos(2)tan(x)sec^{2}(x) + 24{e}^{x}sin^{2}(x)*-sin(2)*0tan(x)sec^{2}(x) + 24{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)(1)sec^{2}(x) + 24{e}^{x}sin^{2}(x)cos(2)tan(x)*2sec^{2}(x)tan(x) + 48({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(x)cos(2)tan(x) + 48{e}^{x}cos(x)cos(x)cos(2)tan(x) + 48{e}^{x}sin(x)*-sin(x)cos(2)tan(x) + 48{e}^{x}sin(x)cos(x)*-sin(2)*0tan(x) + 48{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x)(1) + 24({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)sec^{2}(x) + 24{e}^{x}*2sin(x)cos(x)cos(2)sec^{2}(x) + 24{e}^{x}sin^{2}(x)*-sin(2)*0sec^{2}(x) + 24{e}^{x}sin^{2}(x)cos(2)*2sec^{2}(x)tan(x) + 24({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos^{2}(x)cos(2)tan(x) + 24{e}^{x}*-2cos(x)sin(x)cos(2)tan(x) + 24{e}^{x}cos^{2}(x)*-sin(2)*0tan(x) + 24{e}^{x}cos^{2}(x)cos(2)sec^{2}(x)(1) - 12({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan(x) - 12{e}^{x}*2sin(x)cos(x)cos(2)tan(x) - 12{e}^{x}sin^{2}(x)*-sin(2)*0tan(x) - 12{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)(1) + 24({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(2)cos(x)sec^{2}(x) + 24{e}^{x}cos(x)cos(2)cos(x)sec^{2}(x) + 24{e}^{x}sin(x)*-sin(2)*0cos(x)sec^{2}(x) + 24{e}^{x}sin(x)cos(2)*-sin(x)sec^{2}(x) + 24{e}^{x}sin(x)cos(2)cos(x)*2sec^{2}(x)tan(x) + 24({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(x)cos(2)sec^{2}(x) + 24{e}^{x}cos(x)cos(x)cos(2)sec^{2}(x) + 24{e}^{x}sin(x)*-sin(x)cos(2)sec^{2}(x) + 24{e}^{x}sin(x)cos(x)*-sin(2)*0sec^{2}(x) + 24{e}^{x}sin(x)cos(x)cos(2)*2sec^{2}(x)tan(x) + 24{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 24x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 24x{e}^{x}*2sin(x)cos(x)cos(2)tan(x)sec^{2}(x) + 24x{e}^{x}sin^{2}(x)*-sin(2)*0tan(x)sec^{2}(x) + 24x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)(1)sec^{2}(x) + 24x{e}^{x}sin^{2}(x)cos(2)tan(x)*2sec^{2}(x)tan(x) + 32{e}^{x}sin(x)cos(x)cos(2)tan(x)sec^{2}(x) + 32x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(x)cos(2)tan(x)sec^{2}(x) + 32x{e}^{x}cos(x)cos(x)cos(2)tan(x)sec^{2}(x) + 32x{e}^{x}sin(x)*-sin(x)cos(2)tan(x)sec^{2}(x) + 32x{e}^{x}sin(x)cos(x)*-sin(2)*0tan(x)sec^{2}(x) + 32x{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x)(1)sec^{2}(x) + 32x{e}^{x}sin(x)cos(x)cos(2)tan(x)*2sec^{2}(x)tan(x) + 8{e}^{x}sin^{2}(x)cos(2)sec^{4}(x) + 8x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)sec^{4}(x) + 8x{e}^{x}*2sin(x)cos(x)cos(2)sec^{4}(x) + 8x{e}^{x}sin^{2}(x)*-sin(2)*0sec^{4}(x) + 8x{e}^{x}sin^{2}(x)cos(2)*4sec^{4}(x)tan(x) + 16{e}^{x}sin^{2}(x)cos(2)tan^{2}(x)sec^{2}(x) + 16x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan^{2}(x)sec^{2}(x) + 16x{e}^{x}*2sin(x)cos(x)cos(2)tan^{2}(x)sec^{2}(x) + 16x{e}^{x}sin^{2}(x)*-sin(2)*0tan^{2}(x)sec^{2}(x) + 16x{e}^{x}sin^{2}(x)cos(2)*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 16x{e}^{x}sin^{2}(x)cos(2)tan^{2}(x)*2sec^{2}(x)tan(x) + 16{e}^{x}sin(x)cos(2)cos(x)tan(x)sec^{2}(x) + 16x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(2)cos(x)tan(x)sec^{2}(x) + 16x{e}^{x}cos(x)cos(2)cos(x)tan(x)sec^{2}(x) + 16x{e}^{x}sin(x)*-sin(2)*0cos(x)tan(x)sec^{2}(x) + 16x{e}^{x}sin(x)cos(2)*-sin(x)tan(x)sec^{2}(x) + 16x{e}^{x}sin(x)cos(2)cos(x)sec^{2}(x)(1)sec^{2}(x) + 16x{e}^{x}sin(x)cos(2)cos(x)tan(x)*2sec^{2}(x)tan(x) + 24{e}^{x}cos^{2}(x)cos(2)tan(x) + 24x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos^{2}(x)cos(2)tan(x) + 24x{e}^{x}*-2cos(x)sin(x)cos(2)tan(x) + 24x{e}^{x}cos^{2}(x)*-sin(2)*0tan(x) + 24x{e}^{x}cos^{2}(x)cos(2)sec^{2}(x)(1) + 24{e}^{x}sin(x)cos(2)cos(x)sec^{2}(x) + 24x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(2)cos(x)sec^{2}(x) + 24x{e}^{x}cos(x)cos(2)cos(x)sec^{2}(x) + 24x{e}^{x}sin(x)*-sin(2)*0cos(x)sec^{2}(x) + 24x{e}^{x}sin(x)cos(2)*-sin(x)sec^{2}(x) + 24x{e}^{x}sin(x)cos(2)cos(x)*2sec^{2}(x)tan(x) - 12{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) - 12x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)sec^{2}(x) - 12x{e}^{x}*2sin(x)cos(x)cos(2)sec^{2}(x) - 12x{e}^{x}sin^{2}(x)*-sin(2)*0sec^{2}(x) - 12x{e}^{x}sin^{2}(x)cos(2)*2sec^{2}(x)tan(x) + 24{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x) + 24x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(x)cos(2)sec^{2}(x) + 24x{e}^{x}cos(x)cos(x)cos(2)sec^{2}(x) + 24x{e}^{x}sin(x)*-sin(x)cos(2)sec^{2}(x) + 24x{e}^{x}sin(x)cos(x)*-sin(2)*0sec^{2}(x) + 24x{e}^{x}sin(x)cos(x)cos(2)*2sec^{2}(x)tan(x) - 20{e}^{x}sin^{2}(x)cos(2)tan(x) - 20x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin^{2}(x)cos(2)tan(x) - 20x{e}^{x}*2sin(x)cos(x)cos(2)tan(x) - 20x{e}^{x}sin^{2}(x)*-sin(2)*0tan(x) - 20x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x)(1) - 8{e}^{x}sin(x)cos(x)cos(2)tan(x) - 8x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))sin(x)cos(x)cos(2)tan(x) - 8x{e}^{x}cos(x)cos(x)cos(2)tan(x) - 8x{e}^{x}sin(x)*-sin(x)cos(2)tan(x) - 8x{e}^{x}sin(x)cos(x)*-sin(2)*0tan(x) - 8x{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x)(1) + 8{e}^{x}cos(2)cos^{2}(x)sec^{2}(x) + 8x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos(2)cos^{2}(x)sec^{2}(x) + 8x{e}^{x}*-sin(2)*0cos^{2}(x)sec^{2}(x) + 8x{e}^{x}cos(2)*-2cos(x)sin(x)sec^{2}(x) + 8x{e}^{x}cos(2)cos^{2}(x)*2sec^{2}(x)tan(x) + 16{e}^{x}cos^{2}(x)cos(2)sec^{2}(x) + 16x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))cos^{2}(x)cos(2)sec^{2}(x) + 16x{e}^{x}*-2cos(x)sin(x)cos(2)sec^{2}(x) + 16x{e}^{x}cos^{2}(x)*-sin(2)*0sec^{2}(x) + 16x{e}^{x}cos^{2}(x)cos(2)*2sec^{2}(x)tan(x)\\=&96{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 128{e}^{x}sin(x)cos(x)cos(2)tan(x)sec^{2}(x) + 32{e}^{x}sin^{2}(x)cos(2)sec^{4}(x) + 64{e}^{x}sin^{2}(x)cos(2)tan^{2}(x)sec^{2}(x) + 64{e}^{x}sin(x)cos(2)cos(x)tan(x)sec^{2}(x) + 96{e}^{x}cos^{2}(x)cos(2)tan(x) + 96{e}^{x}sin(x)cos(2)cos(x)sec^{2}(x) - 48{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) + 96{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x) - 80{e}^{x}sin^{2}(x)cos(2)tan(x) - 32{e}^{x}sin(x)cos(x)cos(2)tan(x) + 32{e}^{x}cos(2)cos^{2}(x)sec^{2}(x) + 64{e}^{x}cos^{2}(x)cos(2)sec^{2}(x) - 48x{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{2}(x) + 128x{e}^{x}sin(x)cos(x)cos(2)tan(x)sec^{2}(x) + 32x{e}^{x}sin^{2}(x)cos(2)sec^{4}(x) + 64x{e}^{x}sin^{2}(x)cos(2)tan^{2}(x)sec^{2}(x) + 80x{e}^{x}cos^{2}(x)cos(2)tan(x)sec^{2}(x) + 32x{e}^{x}sin(x)cos(2)cos(x)sec^{4}(x) + 96x{e}^{x}sin(x)cos(x)cos(2)tan^{2}(x)sec^{2}(x) + 32x{e}^{x}sin(x)cos(x)cos(2)sec^{4}(x) + 64x{e}^{x}sin^{2}(x)cos(2)tan(x)sec^{4}(x) + 32x{e}^{x}sin^{2}(x)cos(2)tan^{3}(x)sec^{2}(x) + 64x{e}^{x}sin(x)cos(2)cos(x)tan(x)sec^{2}(x) + 32x{e}^{x}sin(x)cos(2)cos(x)tan^{2}(x)sec^{2}(x) + 16x{e}^{x}cos(2)cos^{2}(x)tan(x)sec^{2}(x) + 32x{e}^{x}cos(2)cos^{2}(x)sec^{2}(x) + 64x{e}^{x}cos^{2}(x)cos(2)sec^{2}(x) - 80x{e}^{x}sin^{2}(x)cos(2)sec^{2}(x) - 32x{e}^{x}sin(x)cos(x)cos(2)sec^{2}(x) - 96x{e}^{x}sin(x)cos(x)cos(2)tan(x) - 12x{e}^{x}sin^{2}(x)cos(2)tan(x) + 16x{e}^{x}cos^{2}(x)cos(2)tan(x)\\ \end{split}\end{equation} \]