# Gradient of a Function Calculator

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

Enter a function:
Enter the order of variables and/or a point:
If you don't need the order of variables, leave it empty.
If you want a specific order of variables, enter variables comma-separated, like x,y,z.
If you want the gradient at a specific point, for example, at (1, 2, 3), enter it as x,y,z=1,2,3, or simply 1,2,3 if you want the order of variables to be detected automatically.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

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

$$\nabla \left(x^{3} + y^{5}\right) \left(x,y\right)=\left(3 x^{2},5 y^{4}\right)$$$$$\nabla \left(x^{3} + y^{5}\right)|_{\left(x,y\right)=\left(1,7\right)}=\left(3,12005\right)$$$