## 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.

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### 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:

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

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