# Function Gradient Calculator

## Find function gradient step by step

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 $$$f=6 x e^{3}$$$at $$$\left(x,y\right)=\left(2,54\right)$$$**

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

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

$$$\frac{\partial f}{\partial x}=6 e^{3}$$$ (for steps, see derivative calculator)

$$$\frac{\partial f}{\partial y}=0$$$ (for steps, see derivative calculator)

Finally, plug in the point:

$$$\nabla f \left(2,54\right)=\left(6 e^{3},0\right)$$$

### Answer

**$$$\nabla \left(6 x e^{3}\right) \left(x,y\right)=\left(6 e^{3},0\right)$$$**

**$$$\nabla \left(6 x e^{3}\right)|_{\left(x,y\right)=\left(2,54\right)}=\left(6 e^{3},0\right)$$$**