# Gradient of a Function Calculator

The calculator will find the gradient of the given function (at the given point if needed), with steps shown.

## Solution

**Your input: find the gradient of $$$f=x^{3} + y^{5}$$$at $$$\left(x,y\right)=\left(1,7\right)$$$**

To find the gradient of a function (which is a vector), differentiate the function with respect to each variable.

$$$\nabla f = \left(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y}\right)$$$

$$$\frac{\partial f}{\partial x}=3 x^{2}$$$ (for steps, see derivative calculator)

$$$\frac{\partial f}{\partial y}=5 y^{4}$$$ (for steps, see derivative calculator)

Finally, plug in the point:

$$$\nabla f \left(1,7\right)=\left(3,12005\right)$$$

## Answer

**$$$\nabla \left(x^{3} + y^{5}\right) \left(x,y\right)=\left(3 x^{2},5 y^{4}\right)$$$**

**$$$\nabla \left(x^{3} + y^{5}\right)|_{\left(x,y\right)=\left(1,7\right)}=\left(3,12005\right)$$$**