Mathematics
         
语言:中文    Language:English
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.
    Current location:Derivative function > Derivative function calculation history > Answer

    There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {{{{{{{{3}^{4}}^{5}}^{6}}^{7}}^{8}}^{9}}^{10}}^{sin({11}^{sin({12}^{x})})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {-5732048155125366271}^{sin({11}^{sin({12}^{x})})}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( {-5732048155125366271}^{sin({11}^{sin({12}^{x})})}\right)}{dx}\\=&({-5732048155125366271}^{sin({11}^{sin({12}^{x})})}((cos({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})))ln(-5732048155125366271) + \frac{(sin({11}^{sin({12}^{x})}))(0)}{(-5732048155125366271)}))\\=&{12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x})\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x})\right)}{dx}\\=&({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})){11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x}) + {12}^{x}({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})){-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x}) + {12}^{x}{11}^{sin({12}^{x})}({-5732048155125366271}^{sin({11}^{sin({12}^{x})})}((cos({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})))ln(-5732048155125366271) + \frac{(sin({11}^{sin({12}^{x})}))(0)}{(-5732048155125366271)}))ln(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x}) + \frac{{12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}*0ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x})}{(12)} + \frac{{12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln(12)*0ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x})}{(-5732048155125366271)} + \frac{{12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln(12)ln(-5732048155125366271)*0cos({11}^{sin({12}^{x})})cos({12}^{x})}{(11)} + {12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln(12)ln(-5732048155125366271)ln(11)*-sin({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)}))cos({12}^{x}) + {12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})*-sin({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)}))\\=&{12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x}) + {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)cos^{2}({12}^{x})cos({11}^{sin({12}^{x})}) + {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln^{2}(-5732048155125366271)cos^{2}({12}^{x})cos^{2}({11}^{sin({12}^{x})}) - {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{2}({12}^{x}) - {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)sin({12}^{x})cos({11}^{sin({12}^{x})})\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x}) + {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)cos^{2}({12}^{x})cos({11}^{sin({12}^{x})}) + {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln^{2}(-5732048155125366271)cos^{2}({12}^{x})cos^{2}({11}^{sin({12}^{x})}) - {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{2}({12}^{x}) - {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)sin({12}^{x})cos({11}^{sin({12}^{x})})\right)}{dx}\\=&({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})){11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x}) + {12}^{x}({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})){-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x}) + {12}^{x}{11}^{sin({12}^{x})}({-5732048155125366271}^{sin({11}^{sin({12}^{x})})}((cos({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})))ln(-5732048155125366271) + \frac{(sin({11}^{sin({12}^{x})}))(0)}{(-5732048155125366271)}))ln^{2}(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x}) + \frac{{12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}*2ln(12)*0ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x})}{(12)} + \frac{{12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)*0ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x})}{(-5732048155125366271)} + \frac{{12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)*0cos({11}^{sin({12}^{x})})cos({12}^{x})}{(11)} + {12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)*-sin({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)}))cos({12}^{x}) + {12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})*-sin({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})) + ({12}^{(2x)}((2)ln(12) + \frac{(2x)(0)}{(12)})){11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)cos^{2}({12}^{x})cos({11}^{sin({12}^{x})}) + {12}^{(2x)}({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})){-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)cos^{2}({12}^{x})cos({11}^{sin({12}^{x})}) + {12}^{(2x)}{11}^{sin({12}^{x})}({-5732048155125366271}^{sin({11}^{sin({12}^{x})})}((cos({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})))ln(-5732048155125366271) + \frac{(sin({11}^{sin({12}^{x})}))(0)}{(-5732048155125366271)}))ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)cos^{2}({12}^{x})cos({11}^{sin({12}^{x})}) + \frac{{12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}*2ln(11)*0ln^{2}(12)ln(-5732048155125366271)cos^{2}({12}^{x})cos({11}^{sin({12}^{x})})}{(11)} + \frac{{12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)*2ln(12)*0ln(-5732048155125366271)cos^{2}({12}^{x})cos({11}^{sin({12}^{x})})}{(12)} + \frac{{12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)*0cos^{2}({12}^{x})cos({11}^{sin({12}^{x})})}{(-5732048155125366271)} + {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)*-2cos({12}^{x})sin({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)}))cos({11}^{sin({12}^{x})}) + {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)cos^{2}({12}^{x})*-sin({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})) + ({12}^{(2x)}((2)ln(12) + \frac{(2x)(0)}{(12)})){11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln^{2}(-5732048155125366271)cos^{2}({12}^{x})cos^{2}({11}^{sin({12}^{x})}) + {12}^{(2x)}({11}^{(2sin({12}^{x}))}((2cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(2sin({12}^{x}))(0)}{(11)})){-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln^{2}(-5732048155125366271)cos^{2}({12}^{x})cos^{2}({11}^{sin({12}^{x})}) + {12}^{(2x)}{11}^{(2sin({12}^{x}))}({-5732048155125366271}^{sin({11}^{sin({12}^{x})})}((cos({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})))ln(-5732048155125366271) + \frac{(sin({11}^{sin({12}^{x})}))(0)}{(-5732048155125366271)}))ln^{2}(11)ln^{2}(12)ln^{2}(-5732048155125366271)cos^{2}({12}^{x})cos^{2}({11}^{sin({12}^{x})}) + \frac{{12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}*2ln(11)*0ln^{2}(12)ln^{2}(-5732048155125366271)cos^{2}({12}^{x})cos^{2}({11}^{sin({12}^{x})})}{(11)} + \frac{{12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)*2ln(12)*0ln^{2}(-5732048155125366271)cos^{2}({12}^{x})cos^{2}({11}^{sin({12}^{x})})}{(12)} + \frac{{12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)*2ln(-5732048155125366271)*0cos^{2}({12}^{x})cos^{2}({11}^{sin({12}^{x})})}{(-5732048155125366271)} + {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln^{2}(-5732048155125366271)*-2cos({12}^{x})sin({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)}))cos^{2}({11}^{sin({12}^{x})}) + {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln^{2}(-5732048155125366271)cos^{2}({12}^{x})*-2cos({11}^{sin({12}^{x})})sin({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})) - ({12}^{(2x)}((2)ln(12) + \frac{(2x)(0)}{(12)})){11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{2}({12}^{x}) - {12}^{(2x)}({11}^{(2sin({12}^{x}))}((2cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(2sin({12}^{x}))(0)}{(11)})){-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{2}({12}^{x}) - {12}^{(2x)}{11}^{(2sin({12}^{x}))}({-5732048155125366271}^{sin({11}^{sin({12}^{x})})}((cos({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})))ln(-5732048155125366271) + \frac{(sin({11}^{sin({12}^{x})}))(0)}{(-5732048155125366271)}))ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{2}({12}^{x}) - \frac{{12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}*2ln(11)*0ln^{2}(12)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{2}({12}^{x})}{(11)} - \frac{{12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)*2ln(12)*0ln(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{2}({12}^{x})}{(12)} - \frac{{12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)*0sin({11}^{sin({12}^{x})})cos^{2}({12}^{x})}{(-5732048155125366271)} - {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)cos({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)}))cos^{2}({12}^{x}) - {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{2}(12)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})*-2cos({12}^{x})sin({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})) - ({12}^{(2x)}((2)ln(12) + \frac{(2x)(0)}{(12)})){11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)sin({12}^{x})cos({11}^{sin({12}^{x})}) - {12}^{(2x)}({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})){-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)sin({12}^{x})cos({11}^{sin({12}^{x})}) - {12}^{(2x)}{11}^{sin({12}^{x})}({-5732048155125366271}^{sin({11}^{sin({12}^{x})})}((cos({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)})))ln(-5732048155125366271) + \frac{(sin({11}^{sin({12}^{x})}))(0)}{(-5732048155125366271)}))ln^{2}(12)ln(-5732048155125366271)ln(11)sin({12}^{x})cos({11}^{sin({12}^{x})}) - \frac{{12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}*2ln(12)*0ln(-5732048155125366271)ln(11)sin({12}^{x})cos({11}^{sin({12}^{x})})}{(12)} - \frac{{12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)*0ln(11)sin({12}^{x})cos({11}^{sin({12}^{x})})}{(-5732048155125366271)} - \frac{{12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)*0sin({12}^{x})cos({11}^{sin({12}^{x})})}{(11)} - {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)}))cos({11}^{sin({12}^{x})}) - {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(12)ln(-5732048155125366271)ln(11)sin({12}^{x})*-sin({11}^{sin({12}^{x})})({11}^{sin({12}^{x})}((cos({12}^{x})({12}^{x}((1)ln(12) + \frac{(x)(0)}{(12)})))ln(11) + \frac{(sin({12}^{x}))(0)}{(11)}))\\=&{12}^{x}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(12)ln(-5732048155125366271)ln(11)cos({11}^{sin({12}^{x})})cos({12}^{x}) + {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{3}(12)ln(-5732048155125366271)cos^{2}({12}^{x})cos({11}^{sin({12}^{x})}) + {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{3}(12)ln^{2}(-5732048155125366271)cos^{2}({12}^{x})cos^{2}({11}^{sin({12}^{x})}) - 2 * {12}^{(3x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(12)ln(-5732048155125366271)ln^{2}(11)sin({12}^{x})cos({12}^{x})cos({11}^{sin({12}^{x})}) - 2 * {12}^{(3x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(12)ln^{2}(-5732048155125366271)ln^{2}(11)sin({12}^{x})cos({12}^{x})cos^{2}({11}^{sin({12}^{x})}) + 2 * {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(12)ln^{2}(11)ln(-5732048155125366271)cos^{2}({12}^{x})cos({11}^{sin({12}^{x})}) + {12}^{(3x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(11)ln^{3}(12)ln(-5732048155125366271)cos^{3}({12}^{x})cos({11}^{sin({12}^{x})}) + 3 * {12}^{(3x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(11)ln^{3}(12)ln^{2}(-5732048155125366271)cos^{3}({12}^{x})cos^{2}({11}^{sin({12}^{x})}) - 2 * {12}^{(3x)}{11}^{(3sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(11)ln^{3}(12)ln^{2}(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{3}({12}^{x})cos({11}^{sin({12}^{x})}) - {12}^{(3x)}{11}^{(3sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(11)ln^{3}(12)ln^{2}(-5732048155125366271)sin({11}^{sin({12}^{x})})cos({11}^{sin({12}^{x})})cos^{3}({12}^{x}) + 2 * {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(12)ln^{2}(11)ln^{2}(-5732048155125366271)cos^{2}({12}^{x})cos^{2}({11}^{sin({12}^{x})}) + {12}^{(3x)}{11}^{(3sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(11)ln^{3}(12)ln^{3}(-5732048155125366271)cos^{3}({12}^{x})cos^{3}({11}^{sin({12}^{x})}) - {12}^{(3x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{3}(12)ln(-5732048155125366271)sin({12}^{x})cos({12}^{x})cos({11}^{sin({12}^{x})}) - {12}^{(3x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{3}(12)ln^{2}(-5732048155125366271)sin({12}^{x})cos^{2}({11}^{sin({12}^{x})})cos({12}^{x}) - 2 * {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(12)ln^{2}(11)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{2}({12}^{x}) - 3 * {12}^{(3x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(11)ln^{3}(12)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{3}({12}^{x}) - {12}^{(3x)}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}{11}^{(3sin({12}^{x}))}ln^{3}(11)ln^{3}(12)ln(-5732048155125366271)cos^{3}({12}^{x})cos({11}^{sin({12}^{x})}) + 2 * {12}^{(3x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(12)ln(-5732048155125366271)ln^{2}(11)sin({12}^{x})sin({11}^{sin({12}^{x})})cos({12}^{x}) - 3 * {12}^{(2x)}{11}^{sin({12}^{x})}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{3}(12)ln(-5732048155125366271)ln(11)sin({12}^{x})cos({11}^{sin({12}^{x})}) - {12}^{(2x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{3}(12)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})cos^{2}({12}^{x}) - {-5732048155125366271}^{sin({11}^{sin({12}^{x})})}{12}^{(3x)}{11}^{sin({12}^{x})}ln^{3}(12)ln(-5732048155125366271)ln(11)cos({12}^{x})cos({11}^{sin({12}^{x})}) + {12}^{(3x)}{11}^{(2sin({12}^{x}))}{-5732048155125366271}^{sin({11}^{sin({12}^{x})})}ln^{2}(11)ln^{3}(12)ln(-5732048155125366271)sin({11}^{sin({12}^{x})})sin({12}^{x})cos({12}^{x})\\ \end{split}\end{equation} \]



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  New addition:Lenders ToolBox module(Specific location:Math OP > Lenders ToolBox ),welcome。