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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)`.

계산기가 예상대로 작동하지 않았거나 오류를 신고하거나 피드백을 공유하고 싶으시다면 문의해 주세요.

Solution

Your input: find $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)$$$

First, find $$$\frac{\partial}{\partial l}\left(3 x + 4 y\right)$$$

The derivative of a constant is 0:

$${\color{red}{\frac{\partial}{\partial l}\left(3 x + 4 y\right)}}={\color{red}{\left(0\right)}}$$

Thus, $$$\frac{\partial}{\partial l}\left(3 x + 4 y\right)=0$$$

Next, $$$\frac{\partial^{2}}{\partial l \partial a}\left(3 x + 4 y\right)=\frac{\partial}{\partial a} \left(\frac{\partial}{\partial l}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial a}\left(0\right)$$$

The derivative of a constant is 0:

$${\color{red}{\frac{\partial}{\partial a}\left(0\right)}}={\color{red}{\left(0\right)}}$$

Thus, $$$\frac{\partial}{\partial a}\left(0\right)=0$$$

Next, $$$\frac{\partial^{3}}{\partial l \partial a \partial m}\left(3 x + 4 y\right)=\frac{\partial}{\partial m} \left(\frac{\partial^{2}}{\partial l \partial a}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial m}\left(0\right)$$$

The derivative of a constant is 0:

$${\color{red}{\frac{\partial}{\partial m}\left(0\right)}}={\color{red}{\left(0\right)}}$$

Thus, $$$\frac{\partial}{\partial m}\left(0\right)=0$$$

Next, $$$\frac{\partial^{4}}{\partial l \partial a \partial m \partial d}\left(3 x + 4 y\right)=\frac{\partial}{\partial d} \left(\frac{\partial^{3}}{\partial l \partial a \partial m}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial d}\left(0\right)$$$

The derivative of a constant is 0:

$${\color{red}{\frac{\partial}{\partial d}\left(0\right)}}={\color{red}{\left(0\right)}}$$

Thus, $$$\frac{\partial}{\partial d}\left(0\right)=0$$$

Next, $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)=\frac{\partial}{\partial a} \left(\frac{\partial^{4}}{\partial l \partial a \partial m \partial d}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial a}\left(0\right)$$$

The derivative of a constant is 0:

$${\color{red}{\frac{\partial}{\partial a}\left(0\right)}}={\color{red}{\left(0\right)}}$$

Thus, $$$\frac{\partial}{\partial a}\left(0\right)=0$$$

Therefore, $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)=0$$$

Answer: $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)=0$$$