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 7 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/7]Find\ the\ 4th\ derivative\ of\ function\ ax + b\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ax + b\right)}{dx}\\=&a + 0\\=&a\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( a\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[2/7]Find\ the\ 4th\ derivative\ of\ function\ axx + bx + c\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ax^{2} + bx + c\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ax^{2} + bx + c\right)}{dx}\\=&a*2x + b + 0\\=&2ax + b\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2ax + b\right)}{dx}\\=&2a + 0\\=&2a\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2a\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[3/7]Find\ the\ 4th\ derivative\ of\ function\ \frac{a}{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{a}{x}\right)}{dx}\\=&\frac{a*-1}{x^{2}}\\=&\frac{-a}{x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-a}{x^{2}}\right)}{dx}\\=&\frac{-a*-2}{x^{3}}\\=&\frac{2a}{x^{3}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2a}{x^{3}}\right)}{dx}\\=&\frac{2a*-3}{x^{4}}\\=&\frac{-6a}{x^{4}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6a}{x^{4}}\right)}{dx}\\=&\frac{-6a*-4}{x^{5}}\\=&\frac{24a}{x^{5}}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[4/7]Find\ the\ 4th\ derivative\ of\ function\ xxx\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{3}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{3}\right)}{dx}\\=&3x^{2}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3x^{2}\right)}{dx}\\=&3*2x\\=&6x\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 6x\right)}{dx}\\=&6\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 6\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[5/7]Find\ the\ 4th\ derivative\ of\ function\ xxxx\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{4}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{4}\right)}{dx}\\=&4x^{3}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 4x^{3}\right)}{dx}\\=&4*3x^{2}\\=&12x^{2}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 12x^{2}\right)}{dx}\\=&12*2x\\=&24x\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 24x\right)}{dx}\\=&24\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[6/7]Find\ the\ 4th\ derivative\ of\ function\ sqrt(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(x)\right)}{dx}\\=&\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}}\\=&\frac{1}{2x^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{2x^{\frac{1}{2}}}\right)}{dx}\\=&\frac{\frac{-1}{2}}{2x^{\frac{3}{2}}}\\=&\frac{-1}{4x^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{4x^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-\frac{-3}{2}}{4x^{\frac{5}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{\frac{3}{8}}{x^{\frac{5}{2}}}\right)}{dx}\\=&\frac{\frac{3}{8}*\frac{-5}{2}}{x^{\frac{7}{2}}}\\=&\frac{-15}{16x^{\frac{7}{2}}}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[7/7]Find\ the\ 4th\ derivative\ of\ function\ e^{xx}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{x^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{x^{2}}\right)}{dx}\\=&e^{x^{2}}*2x\\=&2xe^{x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2xe^{x^{2}}\right)}{dx}\\=&2e^{x^{2}} + 2xe^{x^{2}}*2x\\=&2e^{x^{2}} + 4x^{2}e^{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2e^{x^{2}} + 4x^{2}e^{x^{2}}\right)}{dx}\\=&2e^{x^{2}}*2x + 4*2xe^{x^{2}} + 4x^{2}e^{x^{2}}*2x\\=&12xe^{x^{2}} + 8x^{3}e^{x^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 12xe^{x^{2}} + 8x^{3}e^{x^{2}}\right)}{dx}\\=&12e^{x^{2}} + 12xe^{x^{2}}*2x + 8*3x^{2}e^{x^{2}} + 8x^{3}e^{x^{2}}*2x\\=&12e^{x^{2}} + 48x^{2}e^{x^{2}} + 16x^{4}e^{x^{2}}\\ \end{split}\end{equation} \]
>>注：本次最多计算 7 道题。
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/7]Find\ the\ 4th\ derivative\ of\ function\ ax + b\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ax + b\right)}{dx}\\=&a + 0\\=&a\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( a\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[2/7]Find\ the\ 4th\ derivative\ of\ function\ axx + bx + c\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ax^{2} + bx + c\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ax^{2} + bx + c\right)}{dx}\\=&a*2x + b + 0\\=&2ax + b\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2ax + b\right)}{dx}\\=&2a + 0\\=&2a\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2a\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[3/7]Find\ the\ 4th\ derivative\ of\ function\ \frac{a}{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{a}{x}\right)}{dx}\\=&\frac{a*-1}{x^{2}}\\=&\frac{-a}{x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-a}{x^{2}}\right)}{dx}\\=&\frac{-a*-2}{x^{3}}\\=&\frac{2a}{x^{3}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2a}{x^{3}}\right)}{dx}\\=&\frac{2a*-3}{x^{4}}\\=&\frac{-6a}{x^{4}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6a}{x^{4}}\right)}{dx}\\=&\frac{-6a*-4}{x^{5}}\\=&\frac{24a}{x^{5}}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[4/7]Find\ the\ 4th\ derivative\ of\ function\ xxx\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{3}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{3}\right)}{dx}\\=&3x^{2}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3x^{2}\right)}{dx}\\=&3*2x\\=&6x\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 6x\right)}{dx}\\=&6\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 6\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[5/7]Find\ the\ 4th\ derivative\ of\ function\ xxxx\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{4}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{4}\right)}{dx}\\=&4x^{3}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 4x^{3}\right)}{dx}\\=&4*3x^{2}\\=&12x^{2}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 12x^{2}\right)}{dx}\\=&12*2x\\=&24x\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 24x\right)}{dx}\\=&24\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[6/7]Find\ the\ 4th\ derivative\ of\ function\ sqrt(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(x)\right)}{dx}\\=&\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}}\\=&\frac{1}{2x^{\frac{1}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{2x^{\frac{1}{2}}}\right)}{dx}\\=&\frac{\frac{-1}{2}}{2x^{\frac{3}{2}}}\\=&\frac{-1}{4x^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{4x^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-\frac{-3}{2}}{4x^{\frac{5}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{\frac{3}{8}}{x^{\frac{5}{2}}}\right)}{dx}\\=&\frac{\frac{3}{8}*\frac{-5}{2}}{x^{\frac{7}{2}}}\\=&\frac{-15}{16x^{\frac{7}{2}}}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}[7/7]Find\ the\ 4th\ derivative\ of\ function\ e^{xx}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{x^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{x^{2}}\right)}{dx}\\=&e^{x^{2}}*2x\\=&2xe^{x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2xe^{x^{2}}\right)}{dx}\\=&2e^{x^{2}} + 2xe^{x^{2}}*2x\\=&2e^{x^{2}} + 4x^{2}e^{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2e^{x^{2}} + 4x^{2}e^{x^{2}}\right)}{dx}\\=&2e^{x^{2}}*2x + 4*2xe^{x^{2}} + 4x^{2}e^{x^{2}}*2x\\=&12xe^{x^{2}} + 8x^{3}e^{x^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 12xe^{x^{2}} + 8x^{3}e^{x^{2}}\right)}{dx}\\=&12e^{x^{2}} + 12xe^{x^{2}}*2x + 8*3x^{2}e^{x^{2}} + 8x^{3}e^{x^{2}}*2x\\=&12e^{x^{2}} + 48x^{2}e^{x^{2}} + 16x^{4}e^{x^{2}}\\ \end{split}\end{equation} \]
>>注：本次最多计算 7 道题。