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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{140xxxx + 160000xxx + 66000000xx + 12000000000x + 860000000000}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}\right)}{dx}\\=&e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0)\\=&560x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 480000x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 132000000xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 12000000000e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 560x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 480000x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 132000000xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 12000000000e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}\right)}{dx}\\=&560*3x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 560x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 480000*2xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 480000x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 132000000e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 132000000xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 12000000000e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0)\\=&28944000000001680x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 313600x^{6}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 537600000x^{5}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 378240000000x^{4}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 140160000000000x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 3168000000000960000xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 3573952589544412928e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 28944000000001680x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 313600x^{6}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 537600000x^{5}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 378240000000x^{4}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 140160000000000x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 3168000000000960000xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 3573952589544412928e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}\right)}{dx}\\=&28944000000001680*2xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 28944000000001680x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 313600*6x^{5}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 313600x^{6}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 537600000*5x^{4}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 537600000x^{5}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 378240000000*4x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 378240000000x^{4}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 140160000000000*3x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 140160000000000x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 3168000000000960000e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 3168000000000960000xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) - 3573952589544412928e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0)\\=&3604077161111293216xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 7709632589673590528x^{5}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 5930933361392709632x^{4}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 3750704868531781632x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 5525514218019913728x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 175616000x^{9}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 451584000000x^{8}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 511257600000000x^{7}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 334771200000000000x^{6}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 95730013427901952e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 3604077161111293216xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 7709632589673590528x^{5}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 5930933361392709632x^{4}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 3750704868531781632x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 5525514218019913728x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 175616000x^{9}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 451584000000x^{8}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 511257600000000x^{7}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 334771200000000000x^{6}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 95730013427901952e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}\right)}{dx}\\=&3604077161111293216e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 3604077161111293216xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) - 7709632589673590528*5x^{4}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 7709632589673590528x^{5}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 5930933361392709632*4x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 5930933361392709632x^{4}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 3750704868531781632*3x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 3750704868531781632x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) - 5525514218019913728*2xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 5525514218019913728x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 175616000*9x^{8}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 175616000x^{9}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 451584000000*8x^{7}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 451584000000x^{8}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 511257600000000*7x^{6}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 511257600000000x^{7}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 334771200000000000*6x^{5}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 334771200000000000x^{6}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0) + 95730013427901952e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}(140*4x^{3} + 160000*3x^{2} + 66000000*2x + 12000000000 + 0)\\=&5787409525731691808e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 8717909348332598528x^{4}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 7150737519410528256x^{3}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 5156127490851545088x^{2}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 6003002506555686912xe^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 3210857648352813056x^{8}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 7907800006259638272x^{7}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 8489073880597921792x^{6}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 4733082815185289216x^{5}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 98344960000x^{12}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 337182720000000x^{11}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} + 526245888000000000x^{10}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000} - 3470089990157893632x^{9}e^{140x^{4} + 160000x^{3} + 66000000x^{2} + 12000000000x + 860000000000}\\ \end{split}\end{equation} \]