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Partial Derivative Calculator

Calculate partial derivatives step by step

This online calculator will calculate the partial derivative of the function, with steps shown. You can specify any order of integration.

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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)`.

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Solution

Your input: find $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(81 x^{2} + y^{2}\right)$$$

First, find $$$\frac{\partial}{\partial l}\left(81 x^{2} + y^{2}\right)$$$

The derivative of a constant is 0:

$${\color{red}{\frac{\partial}{\partial l}\left(81 x^{2} + y^{2}\right)}}={\color{red}{\left(0\right)}}$$

Thus, $$$\frac{\partial}{\partial l}\left(81 x^{2} + y^{2}\right)=0$$$

Next, $$$\frac{\partial^{2}}{\partial l \partial a}\left(81 x^{2} + y^{2}\right)=\frac{\partial}{\partial a} \left(\frac{\partial}{\partial l}\left(81 x^{2} + y^{2}\right) \right)=\frac{\partial}{\partial a}\left(0\right)$$$

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, $$$\frac{\partial^{3}}{\partial l \partial a \partial m}\left(81 x^{2} + y^{2}\right)=\frac{\partial}{\partial m} \left(\frac{\partial^{2}}{\partial l \partial a}\left(81 x^{2} + y^{2}\right) \right)=\frac{\partial}{\partial m}\left(0\right)$$$

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, $$$\frac{\partial^{4}}{\partial l \partial a \partial m \partial d}\left(81 x^{2} + y^{2}\right)=\frac{\partial}{\partial d} \left(\frac{\partial^{3}}{\partial l \partial a \partial m}\left(81 x^{2} + y^{2}\right) \right)=\frac{\partial}{\partial d}\left(0\right)$$$

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, $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(81 x^{2} + y^{2}\right)=\frac{\partial}{\partial a} \left(\frac{\partial^{4}}{\partial l \partial a \partial m \partial d}\left(81 x^{2} + y^{2}\right) \right)=\frac{\partial}{\partial a}\left(0\right)$$$

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, $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(81 x^{2} + y^{2}\right)=0$$$

Answer: $$$\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(81 x^{2} + y^{2}\right)=0$$$