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  2. Kalkylatorer
  3. Kalkylatorer: Analys III
  4. Analyskalkylator

Kalkylator för funktionens gradient

Hitta funktionens gradient steg för steg

Kalkylatorn kommer att hitta gradienten för den givna funktionen (i den givna punkten om det behövs), med visade steg.

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 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

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

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