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  1. 홈
  2. 계산기
  3. 계산기: 미적분학 III
  4. 미적분 계산기

편도함수 계산기

편도함수를 단계별로 계산

이 온라인 계산기는 풀이 과정을 보여 주면서 함수의 편미분을 계산합니다. 적분의 순서는 임의로 지정할 수 있습니다.

Enter a function:

Enter the order of integration:

Hint: type x^2,y to calculate `(partial^3 f)/(partial x^2 partial y)`, or enter x,y^2,x to find `(partial^4 f)/(partial x partial y^2 partial x)`.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: find $$$\frac{\partial}{\partial x}\left(x^{2} y^{2}\right)$$$

Apply the constant multiple rule $$$\frac{\partial}{\partial x} \left(c \cdot f \right)=c \cdot \frac{\partial}{\partial x} \left(f \right)$$$ with $$$c=y^{2}$$$ and $$$f=x^{2}$$$:

$${\color{red}{\frac{\partial}{\partial x}\left(x^{2} y^{2}\right)}}={\color{red}{y^{2} \frac{\partial}{\partial x}\left(x^{2}\right)}}$$

Apply the power rule $$$\frac{\partial}{\partial x} \left(x^{n} \right)=n\cdot x^{-1+n}$$$ with $$$n=2$$$:

$$y^{2} {\color{red}{\frac{\partial}{\partial x}\left(x^{2}\right)}}=y^{2} {\color{red}{\left(2 x^{-1 + 2}\right)}}=2 x y^{2}$$

Thus, $$$\frac{\partial}{\partial x}\left(x^{2} y^{2}\right)=2 x y^{2}$$$

Answer: $$$\frac{\partial}{\partial x}\left(x^{2} y^{2}\right)=2 x y^{2}$$$


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