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 1 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ h - h(10{(\frac{(x - A - B)}{C})}^{3} - 15{(\frac{(x - A - B)}{C})}^{4} + 6{(\frac{(x - A - B)}{C})}^{5})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{10hx^{3}}{C^{3}} + \frac{30hAx^{2}}{C^{3}} + \frac{30hBx^{2}}{C^{3}} - \frac{30hA^{2}x}{C^{3}} - \frac{60hABx}{C^{3}} - \frac{30hB^{2}x}{C^{3}} - \frac{60hAx^{3}}{C^{4}} + \frac{180hABx^{2}}{C^{4}} - \frac{180hA^{2}Bx}{C^{4}} - \frac{60hBx^{3}}{C^{4}} + \frac{15hx^{4}}{C^{4}} + \frac{90hA^{2}x^{2}}{C^{4}} + \frac{90hB^{2}x^{2}}{C^{4}} - \frac{60hA^{3}x}{C^{4}} - \frac{180hAB^{2}x}{C^{4}} - \frac{60hB^{3}x}{C^{4}} + \frac{30hAx^{4}}{C^{5}} - \frac{120hABx^{3}}{C^{5}} + \frac{180hA^{2}Bx^{2}}{C^{5}} + \frac{30hBx^{4}}{C^{5}} - \frac{60hA^{2}x^{3}}{C^{5}} + \frac{180hAB^{2}x^{2}}{C^{5}} - \frac{120hA^{3}Bx}{C^{5}} - \frac{180hA^{2}B^{2}x}{C^{5}} - \frac{60hB^{2}x^{3}}{C^{5}} - \frac{6hx^{5}}{C^{5}} + \frac{60hA^{3}x^{2}}{C^{5}} + \frac{60hB^{3}x^{2}}{C^{5}} - \frac{30hA^{4}x}{C^{5}} - \frac{120hAB^{3}x}{C^{5}} - \frac{30hB^{4}x}{C^{5}} + \frac{10hA^{3}}{C^{3}} + \frac{30hA^{2}B}{C^{3}} + \frac{60hA^{3}B}{C^{4}} + \frac{10hB^{3}}{C^{3}} + \frac{15hA^{4}}{C^{4}} + \frac{90hA^{2}B^{2}}{C^{4}} + \frac{60hAB^{3}}{C^{4}} + \frac{30hAB^{2}}{C^{3}} + \frac{15hB^{4}}{C^{4}} + \frac{6hA^{5}}{C^{5}} + \frac{30hA^{4}B}{C^{5}} + \frac{60hA^{3}B^{2}}{C^{5}} + \frac{60hA^{2}B^{3}}{C^{5}} + \frac{30hAB^{4}}{C^{5}} + \frac{6hB^{5}}{C^{5}} + h\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{10hx^{3}}{C^{3}} + \frac{30hAx^{2}}{C^{3}} + \frac{30hBx^{2}}{C^{3}} - \frac{30hA^{2}x}{C^{3}} - \frac{60hABx}{C^{3}} - \frac{30hB^{2}x}{C^{3}} - \frac{60hAx^{3}}{C^{4}} + \frac{180hABx^{2}}{C^{4}} - \frac{180hA^{2}Bx}{C^{4}} - \frac{60hBx^{3}}{C^{4}} + \frac{15hx^{4}}{C^{4}} + \frac{90hA^{2}x^{2}}{C^{4}} + \frac{90hB^{2}x^{2}}{C^{4}} - \frac{60hA^{3}x}{C^{4}} - \frac{180hAB^{2}x}{C^{4}} - \frac{60hB^{3}x}{C^{4}} + \frac{30hAx^{4}}{C^{5}} - \frac{120hABx^{3}}{C^{5}} + \frac{180hA^{2}Bx^{2}}{C^{5}} + \frac{30hBx^{4}}{C^{5}} - \frac{60hA^{2}x^{3}}{C^{5}} + \frac{180hAB^{2}x^{2}}{C^{5}} - \frac{120hA^{3}Bx}{C^{5}} - \frac{180hA^{2}B^{2}x}{C^{5}} - \frac{60hB^{2}x^{3}}{C^{5}} - \frac{6hx^{5}}{C^{5}} + \frac{60hA^{3}x^{2}}{C^{5}} + \frac{60hB^{3}x^{2}}{C^{5}} - \frac{30hA^{4}x}{C^{5}} - \frac{120hAB^{3}x}{C^{5}} - \frac{30hB^{4}x}{C^{5}} + \frac{10hA^{3}}{C^{3}} + \frac{30hA^{2}B}{C^{3}} + \frac{60hA^{3}B}{C^{4}} + \frac{10hB^{3}}{C^{3}} + \frac{15hA^{4}}{C^{4}} + \frac{90hA^{2}B^{2}}{C^{4}} + \frac{60hAB^{3}}{C^{4}} + \frac{30hAB^{2}}{C^{3}} + \frac{15hB^{4}}{C^{4}} + \frac{6hA^{5}}{C^{5}} + \frac{30hA^{4}B}{C^{5}} + \frac{60hA^{3}B^{2}}{C^{5}} + \frac{60hA^{2}B^{3}}{C^{5}} + \frac{30hAB^{4}}{C^{5}} + \frac{6hB^{5}}{C^{5}} + h\right)}{dx}\\=& - \frac{10h*3x^{2}}{C^{3}} + \frac{30hA*2x}{C^{3}} + \frac{30hB*2x}{C^{3}} - \frac{30hA^{2}}{C^{3}} - \frac{60hAB}{C^{3}} - \frac{30hB^{2}}{C^{3}} - \frac{60hA*3x^{2}}{C^{4}} + \frac{180hAB*2x}{C^{4}} - \frac{180hA^{2}B}{C^{4}} - \frac{60hB*3x^{2}}{C^{4}} + \frac{15h*4x^{3}}{C^{4}} + \frac{90hA^{2}*2x}{C^{4}} + \frac{90hB^{2}*2x}{C^{4}} - \frac{60hA^{3}}{C^{4}} - \frac{180hAB^{2}}{C^{4}} - \frac{60hB^{3}}{C^{4}} + \frac{30hA*4x^{3}}{C^{5}} - \frac{120hAB*3x^{2}}{C^{5}} + \frac{180hA^{2}B*2x}{C^{5}} + \frac{30hB*4x^{3}}{C^{5}} - \frac{60hA^{2}*3x^{2}}{C^{5}} + \frac{180hAB^{2}*2x}{C^{5}} - \frac{120hA^{3}B}{C^{5}} - \frac{180hA^{2}B^{2}}{C^{5}} - \frac{60hB^{2}*3x^{2}}{C^{5}} - \frac{6h*5x^{4}}{C^{5}} + \frac{60hA^{3}*2x}{C^{5}} + \frac{60hB^{3}*2x}{C^{5}} - \frac{30hA^{4}}{C^{5}} - \frac{120hAB^{3}}{C^{5}} - \frac{30hB^{4}}{C^{5}} + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0\\=& - \frac{30hx^{2}}{C^{3}} + \frac{60hAx}{C^{3}} + \frac{60hBx}{C^{3}} - \frac{180hAx^{2}}{C^{4}} + \frac{360hABx}{C^{4}} - \frac{180hBx^{2}}{C^{4}} + \frac{180hA^{2}x}{C^{4}} - \frac{360hABx^{2}}{C^{5}} + \frac{360hA^{2}Bx}{C^{5}} + \frac{180hB^{2}x}{C^{4}} + \frac{60hx^{3}}{C^{4}} + \frac{120hAx^{3}}{C^{5}} + \frac{120hBx^{3}}{C^{5}} - \frac{180hA^{2}x^{2}}{C^{5}} + \frac{360hAB^{2}x}{C^{5}} - \frac{180hB^{2}x^{2}}{C^{5}} + \frac{120hA^{3}x}{C^{5}} - \frac{60hAB}{C^{3}} - \frac{180hA^{2}B}{C^{4}} + \frac{120hB^{3}x}{C^{5}} - \frac{60hA^{3}}{C^{4}} - \frac{180hAB^{2}}{C^{4}} - \frac{120hA^{3}B}{C^{5}} - \frac{180hA^{2}B^{2}}{C^{5}} - \frac{60hB^{3}}{C^{4}} - \frac{30hx^{4}}{C^{5}} - \frac{30hA^{2}}{C^{3}} - \frac{30hB^{2}}{C^{3}} - \frac{30hA^{4}}{C^{5}} - \frac{120hAB^{3}}{C^{5}} - \frac{30hB^{4}}{C^{5}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ h - h(10{(\frac{(x - A - B)}{C})}^{3} - 15{(\frac{(x - A - B)}{C})}^{4} + 6{(\frac{(x - A - B)}{C})}^{5})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{10hx^{3}}{C^{3}} + \frac{30hAx^{2}}{C^{3}} + \frac{30hBx^{2}}{C^{3}} - \frac{30hA^{2}x}{C^{3}} - \frac{60hABx}{C^{3}} - \frac{30hB^{2}x}{C^{3}} - \frac{60hAx^{3}}{C^{4}} + \frac{180hABx^{2}}{C^{4}} - \frac{180hA^{2}Bx}{C^{4}} - \frac{60hBx^{3}}{C^{4}} + \frac{15hx^{4}}{C^{4}} + \frac{90hA^{2}x^{2}}{C^{4}} + \frac{90hB^{2}x^{2}}{C^{4}} - \frac{60hA^{3}x}{C^{4}} - \frac{180hAB^{2}x}{C^{4}} - \frac{60hB^{3}x}{C^{4}} + \frac{30hAx^{4}}{C^{5}} - \frac{120hABx^{3}}{C^{5}} + \frac{180hA^{2}Bx^{2}}{C^{5}} + \frac{30hBx^{4}}{C^{5}} - \frac{60hA^{2}x^{3}}{C^{5}} + \frac{180hAB^{2}x^{2}}{C^{5}} - \frac{120hA^{3}Bx}{C^{5}} - \frac{180hA^{2}B^{2}x}{C^{5}} - \frac{60hB^{2}x^{3}}{C^{5}} - \frac{6hx^{5}}{C^{5}} + \frac{60hA^{3}x^{2}}{C^{5}} + \frac{60hB^{3}x^{2}}{C^{5}} - \frac{30hA^{4}x}{C^{5}} - \frac{120hAB^{3}x}{C^{5}} - \frac{30hB^{4}x}{C^{5}} + \frac{10hA^{3}}{C^{3}} + \frac{30hA^{2}B}{C^{3}} + \frac{60hA^{3}B}{C^{4}} + \frac{10hB^{3}}{C^{3}} + \frac{15hA^{4}}{C^{4}} + \frac{90hA^{2}B^{2}}{C^{4}} + \frac{60hAB^{3}}{C^{4}} + \frac{30hAB^{2}}{C^{3}} + \frac{15hB^{4}}{C^{4}} + \frac{6hA^{5}}{C^{5}} + \frac{30hA^{4}B}{C^{5}} + \frac{60hA^{3}B^{2}}{C^{5}} + \frac{60hA^{2}B^{3}}{C^{5}} + \frac{30hAB^{4}}{C^{5}} + \frac{6hB^{5}}{C^{5}} + h\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{10hx^{3}}{C^{3}} + \frac{30hAx^{2}}{C^{3}} + \frac{30hBx^{2}}{C^{3}} - \frac{30hA^{2}x}{C^{3}} - \frac{60hABx}{C^{3}} - \frac{30hB^{2}x}{C^{3}} - \frac{60hAx^{3}}{C^{4}} + \frac{180hABx^{2}}{C^{4}} - \frac{180hA^{2}Bx}{C^{4}} - \frac{60hBx^{3}}{C^{4}} + \frac{15hx^{4}}{C^{4}} + \frac{90hA^{2}x^{2}}{C^{4}} + \frac{90hB^{2}x^{2}}{C^{4}} - \frac{60hA^{3}x}{C^{4}} - \frac{180hAB^{2}x}{C^{4}} - \frac{60hB^{3}x}{C^{4}} + \frac{30hAx^{4}}{C^{5}} - \frac{120hABx^{3}}{C^{5}} + \frac{180hA^{2}Bx^{2}}{C^{5}} + \frac{30hBx^{4}}{C^{5}} - \frac{60hA^{2}x^{3}}{C^{5}} + \frac{180hAB^{2}x^{2}}{C^{5}} - \frac{120hA^{3}Bx}{C^{5}} - \frac{180hA^{2}B^{2}x}{C^{5}} - \frac{60hB^{2}x^{3}}{C^{5}} - \frac{6hx^{5}}{C^{5}} + \frac{60hA^{3}x^{2}}{C^{5}} + \frac{60hB^{3}x^{2}}{C^{5}} - \frac{30hA^{4}x}{C^{5}} - \frac{120hAB^{3}x}{C^{5}} - \frac{30hB^{4}x}{C^{5}} + \frac{10hA^{3}}{C^{3}} + \frac{30hA^{2}B}{C^{3}} + \frac{60hA^{3}B}{C^{4}} + \frac{10hB^{3}}{C^{3}} + \frac{15hA^{4}}{C^{4}} + \frac{90hA^{2}B^{2}}{C^{4}} + \frac{60hAB^{3}}{C^{4}} + \frac{30hAB^{2}}{C^{3}} + \frac{15hB^{4}}{C^{4}} + \frac{6hA^{5}}{C^{5}} + \frac{30hA^{4}B}{C^{5}} + \frac{60hA^{3}B^{2}}{C^{5}} + \frac{60hA^{2}B^{3}}{C^{5}} + \frac{30hAB^{4}}{C^{5}} + \frac{6hB^{5}}{C^{5}} + h\right)}{dx}\\=& - \frac{10h*3x^{2}}{C^{3}} + \frac{30hA*2x}{C^{3}} + \frac{30hB*2x}{C^{3}} - \frac{30hA^{2}}{C^{3}} - \frac{60hAB}{C^{3}} - \frac{30hB^{2}}{C^{3}} - \frac{60hA*3x^{2}}{C^{4}} + \frac{180hAB*2x}{C^{4}} - \frac{180hA^{2}B}{C^{4}} - \frac{60hB*3x^{2}}{C^{4}} + \frac{15h*4x^{3}}{C^{4}} + \frac{90hA^{2}*2x}{C^{4}} + \frac{90hB^{2}*2x}{C^{4}} - \frac{60hA^{3}}{C^{4}} - \frac{180hAB^{2}}{C^{4}} - \frac{60hB^{3}}{C^{4}} + \frac{30hA*4x^{3}}{C^{5}} - \frac{120hAB*3x^{2}}{C^{5}} + \frac{180hA^{2}B*2x}{C^{5}} + \frac{30hB*4x^{3}}{C^{5}} - \frac{60hA^{2}*3x^{2}}{C^{5}} + \frac{180hAB^{2}*2x}{C^{5}} - \frac{120hA^{3}B}{C^{5}} - \frac{180hA^{2}B^{2}}{C^{5}} - \frac{60hB^{2}*3x^{2}}{C^{5}} - \frac{6h*5x^{4}}{C^{5}} + \frac{60hA^{3}*2x}{C^{5}} + \frac{60hB^{3}*2x}{C^{5}} - \frac{30hA^{4}}{C^{5}} - \frac{120hAB^{3}}{C^{5}} - \frac{30hB^{4}}{C^{5}} + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0\\=& - \frac{30hx^{2}}{C^{3}} + \frac{60hAx}{C^{3}} + \frac{60hBx}{C^{3}} - \frac{180hAx^{2}}{C^{4}} + \frac{360hABx}{C^{4}} - \frac{180hBx^{2}}{C^{4}} + \frac{180hA^{2}x}{C^{4}} - \frac{360hABx^{2}}{C^{5}} + \frac{360hA^{2}Bx}{C^{5}} + \frac{180hB^{2}x}{C^{4}} + \frac{60hx^{3}}{C^{4}} + \frac{120hAx^{3}}{C^{5}} + \frac{120hBx^{3}}{C^{5}} - \frac{180hA^{2}x^{2}}{C^{5}} + \frac{360hAB^{2}x}{C^{5}} - \frac{180hB^{2}x^{2}}{C^{5}} + \frac{120hA^{3}x}{C^{5}} - \frac{60hAB}{C^{3}} - \frac{180hA^{2}B}{C^{4}} + \frac{120hB^{3}x}{C^{5}} - \frac{60hA^{3}}{C^{4}} - \frac{180hAB^{2}}{C^{4}} - \frac{120hA^{3}B}{C^{5}} - \frac{180hA^{2}B^{2}}{C^{5}} - \frac{60hB^{3}}{C^{4}} - \frac{30hx^{4}}{C^{5}} - \frac{30hA^{2}}{C^{3}} - \frac{30hB^{2}}{C^{3}} - \frac{30hA^{4}}{C^{5}} - \frac{120hAB^{3}}{C^{5}} - \frac{30hB^{4}}{C^{5}}\\ \end{split}\end{equation} \]