Функціональний калькулятор градієнта

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:

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

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

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