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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ -cos(x - cos({2}^{x}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -cos(x - cos({2}^{x}))\right)}{dx}\\=&--sin(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))\\=&sin(x - cos({2}^{x})) + {2}^{x}ln(2)sin({2}^{x})sin(x - cos({2}^{x}))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( sin(x - cos({2}^{x})) + {2}^{x}ln(2)sin({2}^{x})sin(x - cos({2}^{x}))\right)}{dx}\\=&cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)sin({2}^{x})sin(x - cos({2}^{x})) + \frac{{2}^{x}*0sin({2}^{x})sin(x - cos({2}^{x}))}{(2)} + {2}^{x}ln(2)cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))sin(x - cos({2}^{x})) + {2}^{x}ln(2)sin({2}^{x})cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))\\=&cos(x - cos({2}^{x})) + 2 * {2}^{x}ln(2)sin({2}^{x})cos(x - cos({2}^{x})) + {2}^{x}ln^{2}(2)sin({2}^{x})sin(x - cos({2}^{x})) + {2}^{(2x)}ln^{2}(2)sin(x - cos({2}^{x}))cos({2}^{x}) + {2}^{(2x)}ln^{2}(2)sin^{2}({2}^{x})cos(x - cos({2}^{x}))\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( cos(x - cos({2}^{x})) + 2 * {2}^{x}ln(2)sin({2}^{x})cos(x - cos({2}^{x})) + {2}^{x}ln^{2}(2)sin({2}^{x})sin(x - cos({2}^{x})) + {2}^{(2x)}ln^{2}(2)sin(x - cos({2}^{x}))cos({2}^{x}) + {2}^{(2x)}ln^{2}(2)sin^{2}({2}^{x})cos(x - cos({2}^{x}))\right)}{dx}\\=&-sin(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) + 2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)sin({2}^{x})cos(x - cos({2}^{x})) + \frac{2 * {2}^{x}*0sin({2}^{x})cos(x - cos({2}^{x}))}{(2)} + 2 * {2}^{x}ln(2)cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))cos(x - cos({2}^{x})) + 2 * {2}^{x}ln(2)sin({2}^{x})*-sin(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln^{2}(2)sin({2}^{x})sin(x - cos({2}^{x})) + \frac{{2}^{x}*2ln(2)*0sin({2}^{x})sin(x - cos({2}^{x}))}{(2)} + {2}^{x}ln^{2}(2)cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))sin(x - cos({2}^{x})) + {2}^{x}ln^{2}(2)sin({2}^{x})cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) + ({2}^{(2x)}((2)ln(2) + \frac{(2x)(0)}{(2)}))ln^{2}(2)sin(x - cos({2}^{x}))cos({2}^{x}) + \frac{{2}^{(2x)}*2ln(2)*0sin(x - cos({2}^{x}))cos({2}^{x})}{(2)} + {2}^{(2x)}ln^{2}(2)cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))cos({2}^{x}) + {2}^{(2x)}ln^{2}(2)sin(x - cos({2}^{x}))*-sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + ({2}^{(2x)}((2)ln(2) + \frac{(2x)(0)}{(2)}))ln^{2}(2)sin^{2}({2}^{x})cos(x - cos({2}^{x})) + \frac{{2}^{(2x)}*2ln(2)*0sin^{2}({2}^{x})cos(x - cos({2}^{x}))}{(2)} + {2}^{(2x)}ln^{2}(2)*2sin({2}^{x})cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))cos(x - cos({2}^{x})) + {2}^{(2x)}ln^{2}(2)sin^{2}({2}^{x})*-sin(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))\\=&-sin(x - cos({2}^{x})) - {2}^{x}ln(2)sin({2}^{x})sin(x - cos({2}^{x})) + {2}^{(3x)}ln^{3}(2)sin({2}^{x})cos(x - cos({2}^{x}))cos({2}^{x}) + 2 * {2}^{(2x)}ln^{2}(2)cos({2}^{x})cos(x - cos({2}^{x})) - 2 * {2}^{x}ln(2)sin(x - cos({2}^{x}))sin({2}^{x}) - 2 * {2}^{(2x)}ln^{2}(2)sin^{2}({2}^{x})sin(x - cos({2}^{x})) + {2}^{x}ln^{3}(2)sin({2}^{x})sin(x - cos({2}^{x})) + 2 * {2}^{(3x)}ln^{3}(2)sin({2}^{x})cos({2}^{x})cos(x - cos({2}^{x})) + 3 * {2}^{x}ln^{2}(2)sin({2}^{x})cos(x - cos({2}^{x})) + 3 * {2}^{(2x)}ln^{3}(2)sin^{2}({2}^{x})cos(x - cos({2}^{x})) + 3 * {2}^{(2x)}ln^{3}(2)sin(x - cos({2}^{x}))cos({2}^{x}) + {2}^{(2x)}ln^{2}(2)cos(x - cos({2}^{x}))cos({2}^{x}) - {2}^{(3x)}ln^{3}(2)sin({2}^{x})sin(x - cos({2}^{x})) - {2}^{(2x)}ln^{2}(2)sin(x - cos({2}^{x}))sin^{2}({2}^{x}) - {2}^{(3x)}ln^{3}(2)sin^{3}({2}^{x})sin(x - cos({2}^{x}))\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -sin(x - cos({2}^{x})) - {2}^{x}ln(2)sin({2}^{x})sin(x - cos({2}^{x})) + {2}^{(3x)}ln^{3}(2)sin({2}^{x})cos(x - cos({2}^{x}))cos({2}^{x}) + 2 * {2}^{(2x)}ln^{2}(2)cos({2}^{x})cos(x - cos({2}^{x})) - 2 * {2}^{x}ln(2)sin(x - cos({2}^{x}))sin({2}^{x}) - 2 * {2}^{(2x)}ln^{2}(2)sin^{2}({2}^{x})sin(x - cos({2}^{x})) + {2}^{x}ln^{3}(2)sin({2}^{x})sin(x - cos({2}^{x})) + 2 * {2}^{(3x)}ln^{3}(2)sin({2}^{x})cos({2}^{x})cos(x - cos({2}^{x})) + 3 * {2}^{x}ln^{2}(2)sin({2}^{x})cos(x - cos({2}^{x})) + 3 * {2}^{(2x)}ln^{3}(2)sin^{2}({2}^{x})cos(x - cos({2}^{x})) + 3 * {2}^{(2x)}ln^{3}(2)sin(x - cos({2}^{x}))cos({2}^{x}) + {2}^{(2x)}ln^{2}(2)cos(x - cos({2}^{x}))cos({2}^{x}) - {2}^{(3x)}ln^{3}(2)sin({2}^{x})sin(x - cos({2}^{x})) - {2}^{(2x)}ln^{2}(2)sin(x - cos({2}^{x}))sin^{2}({2}^{x}) - {2}^{(3x)}ln^{3}(2)sin^{3}({2}^{x})sin(x - cos({2}^{x}))\right)}{dx}\\=&-cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) - ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)sin({2}^{x})sin(x - cos({2}^{x})) - \frac{{2}^{x}*0sin({2}^{x})sin(x - cos({2}^{x}))}{(2)} - {2}^{x}ln(2)cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))sin(x - cos({2}^{x})) - {2}^{x}ln(2)sin({2}^{x})cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) + ({2}^{(3x)}((3)ln(2) + \frac{(3x)(0)}{(2)}))ln^{3}(2)sin({2}^{x})cos(x - cos({2}^{x}))cos({2}^{x}) + \frac{{2}^{(3x)}*3ln^{2}(2)*0sin({2}^{x})cos(x - cos({2}^{x}))cos({2}^{x})}{(2)} + {2}^{(3x)}ln^{3}(2)cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))cos(x - cos({2}^{x}))cos({2}^{x}) + {2}^{(3x)}ln^{3}(2)sin({2}^{x})*-sin(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))cos({2}^{x}) + {2}^{(3x)}ln^{3}(2)sin({2}^{x})cos(x - cos({2}^{x}))*-sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + 2({2}^{(2x)}((2)ln(2) + \frac{(2x)(0)}{(2)}))ln^{2}(2)cos({2}^{x})cos(x - cos({2}^{x})) + \frac{2 * {2}^{(2x)}*2ln(2)*0cos({2}^{x})cos(x - cos({2}^{x}))}{(2)} + 2 * {2}^{(2x)}ln^{2}(2)*-sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))cos(x - cos({2}^{x})) + 2 * {2}^{(2x)}ln^{2}(2)cos({2}^{x})*-sin(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) - 2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)sin(x - cos({2}^{x}))sin({2}^{x}) - \frac{2 * {2}^{x}*0sin(x - cos({2}^{x}))sin({2}^{x})}{(2)} - 2 * {2}^{x}ln(2)cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))sin({2}^{x}) - 2 * {2}^{x}ln(2)sin(x - cos({2}^{x}))cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) - 2({2}^{(2x)}((2)ln(2) + \frac{(2x)(0)}{(2)}))ln^{2}(2)sin^{2}({2}^{x})sin(x - cos({2}^{x})) - \frac{2 * {2}^{(2x)}*2ln(2)*0sin^{2}({2}^{x})sin(x - cos({2}^{x}))}{(2)} - 2 * {2}^{(2x)}ln^{2}(2)*2sin({2}^{x})cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))sin(x - cos({2}^{x})) - 2 * {2}^{(2x)}ln^{2}(2)sin^{2}({2}^{x})cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln^{3}(2)sin({2}^{x})sin(x - cos({2}^{x})) + \frac{{2}^{x}*3ln^{2}(2)*0sin({2}^{x})sin(x - cos({2}^{x}))}{(2)} + {2}^{x}ln^{3}(2)cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))sin(x - cos({2}^{x})) + {2}^{x}ln^{3}(2)sin({2}^{x})cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) + 2({2}^{(3x)}((3)ln(2) + \frac{(3x)(0)}{(2)}))ln^{3}(2)sin({2}^{x})cos({2}^{x})cos(x - cos({2}^{x})) + \frac{2 * {2}^{(3x)}*3ln^{2}(2)*0sin({2}^{x})cos({2}^{x})cos(x - cos({2}^{x}))}{(2)} + 2 * {2}^{(3x)}ln^{3}(2)cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))cos({2}^{x})cos(x - cos({2}^{x})) + 2 * {2}^{(3x)}ln^{3}(2)sin({2}^{x})*-sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))cos(x - cos({2}^{x})) + 2 * {2}^{(3x)}ln^{3}(2)sin({2}^{x})cos({2}^{x})*-sin(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) + 3({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln^{2}(2)sin({2}^{x})cos(x - cos({2}^{x})) + \frac{3 * {2}^{x}*2ln(2)*0sin({2}^{x})cos(x - cos({2}^{x}))}{(2)} + 3 * {2}^{x}ln^{2}(2)cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))cos(x - cos({2}^{x})) + 3 * {2}^{x}ln^{2}(2)sin({2}^{x})*-sin(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) + 3({2}^{(2x)}((2)ln(2) + \frac{(2x)(0)}{(2)}))ln^{3}(2)sin^{2}({2}^{x})cos(x - cos({2}^{x})) + \frac{3 * {2}^{(2x)}*3ln^{2}(2)*0sin^{2}({2}^{x})cos(x - cos({2}^{x}))}{(2)} + 3 * {2}^{(2x)}ln^{3}(2)*2sin({2}^{x})cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))cos(x - cos({2}^{x})) + 3 * {2}^{(2x)}ln^{3}(2)sin^{2}({2}^{x})*-sin(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) + 3({2}^{(2x)}((2)ln(2) + \frac{(2x)(0)}{(2)}))ln^{3}(2)sin(x - cos({2}^{x}))cos({2}^{x}) + \frac{3 * {2}^{(2x)}*3ln^{2}(2)*0sin(x - cos({2}^{x}))cos({2}^{x})}{(2)} + 3 * {2}^{(2x)}ln^{3}(2)cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))cos({2}^{x}) + 3 * {2}^{(2x)}ln^{3}(2)sin(x - cos({2}^{x}))*-sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) + ({2}^{(2x)}((2)ln(2) + \frac{(2x)(0)}{(2)}))ln^{2}(2)cos(x - cos({2}^{x}))cos({2}^{x}) + \frac{{2}^{(2x)}*2ln(2)*0cos(x - cos({2}^{x}))cos({2}^{x})}{(2)} + {2}^{(2x)}ln^{2}(2)*-sin(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))cos({2}^{x}) + {2}^{(2x)}ln^{2}(2)cos(x - cos({2}^{x}))*-sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) - ({2}^{(3x)}((3)ln(2) + \frac{(3x)(0)}{(2)}))ln^{3}(2)sin({2}^{x})sin(x - cos({2}^{x})) - \frac{{2}^{(3x)}*3ln^{2}(2)*0sin({2}^{x})sin(x - cos({2}^{x}))}{(2)} - {2}^{(3x)}ln^{3}(2)cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))sin(x - cos({2}^{x})) - {2}^{(3x)}ln^{3}(2)sin({2}^{x})cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))) - ({2}^{(2x)}((2)ln(2) + \frac{(2x)(0)}{(2)}))ln^{2}(2)sin(x - cos({2}^{x}))sin^{2}({2}^{x}) - \frac{{2}^{(2x)}*2ln(2)*0sin(x - cos({2}^{x}))sin^{2}({2}^{x})}{(2)} - {2}^{(2x)}ln^{2}(2)cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))sin^{2}({2}^{x}) - {2}^{(2x)}ln^{2}(2)sin(x - cos({2}^{x}))*2sin({2}^{x})cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})) - ({2}^{(3x)}((3)ln(2) + \frac{(3x)(0)}{(2)}))ln^{3}(2)sin^{3}({2}^{x})sin(x - cos({2}^{x})) - \frac{{2}^{(3x)}*3ln^{2}(2)*0sin^{3}({2}^{x})sin(x - cos({2}^{x}))}{(2)} - {2}^{(3x)}ln^{3}(2)*3sin^{2}({2}^{x})cos({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))sin(x - cos({2}^{x})) - {2}^{(3x)}ln^{3}(2)sin^{3}({2}^{x})cos(x - cos({2}^{x}))(1 - -sin({2}^{x})({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))\\=&-cos(x - cos({2}^{x})) + 6 * {2}^{(3x)}ln^{4}(2)sin({2}^{x})cos(x - cos({2}^{x}))cos({2}^{x}) - 6 * {2}^{(4x)}ln^{4}(2)sin^{2}({2}^{x})sin(x - cos({2}^{x}))cos({2}^{x}) + 12 * {2}^{(3x)}ln^{4}(2)sin({2}^{x})cos({2}^{x})cos(x - cos({2}^{x})) - 4 * {2}^{x}ln(2)sin({2}^{x})cos(x - cos({2}^{x})) + 3 * {2}^{(4x)}ln^{4}(2)cos^{2}({2}^{x})cos(x - cos({2}^{x})) - 3 * {2}^{(3x)}ln^{3}(2)sin(x - cos({2}^{x}))sin({2}^{x})cos({2}^{x}) - 9 * {2}^{(3x)}ln^{3}(2)sin({2}^{x})sin(x - cos({2}^{x}))cos({2}^{x}) + 7 * {2}^{(2x)}ln^{3}(2)cos({2}^{x})cos(x - cos({2}^{x})) - 6 * {2}^{(2x)}ln^{2}(2)sin^{2}({2}^{x})cos(x - cos({2}^{x})) - 6 * {2}^{(2x)}ln^{2}(2)sin(x - cos({2}^{x}))cos({2}^{x}) - {2}^{x}ln^{2}(2)sin({2}^{x})sin(x - cos({2}^{x})) - 5 * {2}^{x}ln^{2}(2)sin(x - cos({2}^{x}))sin({2}^{x}) - 7 * {2}^{(2x)}ln^{3}(2)sin^{2}({2}^{x})sin(x - cos({2}^{x})) - 4 * {2}^{(3x)}ln^{3}(2)sin^{3}({2}^{x})cos(x - cos({2}^{x})) + {2}^{x}ln^{4}(2)sin({2}^{x})sin(x - cos({2}^{x})) + 7 * {2}^{(2x)}ln^{4}(2)sin(x - cos({2}^{x}))cos({2}^{x}) + 4 * {2}^{x}ln^{3}(2)sin({2}^{x})cos(x - cos({2}^{x})) + 7 * {2}^{(2x)}ln^{4}(2)sin^{2}({2}^{x})cos(x - cos({2}^{x})) - 4 * {2}^{(3x)}ln^{3}(2)sin({2}^{x})cos(x - cos({2}^{x})) - 5 * {2}^{(2x)}ln^{3}(2)sin(x - cos({2}^{x}))sin^{2}({2}^{x}) - 6 * {2}^{(3x)}ln^{4}(2)sin^{3}({2}^{x})sin(x - cos({2}^{x})) + 5 * {2}^{(2x)}ln^{3}(2)cos(x - cos({2}^{x}))cos({2}^{x}) - 4 * {2}^{(4x)}ln^{4}(2)sin^{2}({2}^{x})cos(x - cos({2}^{x})) - 6 * {2}^{(3x)}ln^{4}(2)sin({2}^{x})sin(x - cos({2}^{x})) - {2}^{(4x)}ln^{4}(2)sin(x - cos({2}^{x}))cos({2}^{x}) - {2}^{(4x)}ln^{4}(2)sin^{4}({2}^{x})cos(x - cos({2}^{x}))\\ \end{split}\end{equation} \]