No AI is used
  1. Home
  2. Calculators
  3. Calculators: Calculus III
  4. Calculus Calculator

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 didn't work as expected, or you'd like to report an error or share feedback, please contact us.

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:

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

Answer

$$$\nabla \left(x^{3} + y^{5}\right) \left(x,y\right)=\left(3 x^{2},5 y^{4}\right)$$$

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