# 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 $$$f=e^{x} + \sin{\left(y z \right)}$$$at $$$\left(x,y,z\right)=\left(3,0,\frac{\pi}{3}\right)$$$**

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

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

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

$$$\frac{\partial f}{\partial y}=z \cos{\left(y z \right)}$$$ (for steps, see derivative calculator)

$$$\frac{\partial f}{\partial z}=y \cos{\left(y z \right)}$$$ (for steps, see derivative calculator)

Finally, plug in the point:

$$$\nabla f \left(3,0,\frac{\pi}{3}\right)=\left(e^{3},\frac{\pi}{3},0\right)$$$

### Answer

**$$$\nabla \left(e^{x} + \sin{\left(y z \right)}\right) \left(x,y,z\right)=\left(e^{x},z \cos{\left(y z \right)},y \cos{\left(y z \right)}\right)$$$**

**$$$\nabla \left(e^{x} + \sin{\left(y z \right)}\right)|_{\left(x,y,z\right)=\left(3,0,\frac{\pi}{3}\right)}=\left(e^{3},\frac{\pi}{3},0\right)$$$**