# 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.

### Solution

**Your input: find $$$\frac{\partial}{\partial y}\left(81 x^{2} + y^{2}\right)$$$**

**The derivative of a sum/difference is the sum/difference of derivatives:**

**The derivative of a constant is 0:**

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

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

**Answer:** $$$\frac{\partial}{\partial y}\left(81 x^{2} + y^{2}\right)=2 y$$$