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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.

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:

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

Answer

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

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