## 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.

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 $f=6 x e^{3}$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:

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

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