Calculadora de gradiente de função
Encontrar gradiente de função passo a passo
A calculadora encontrará o gradiente da função dada (no ponto dado, se necessário), com as etapas mostradas.
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
$$$\nabla \left(x^{3} + y^{5}\right) \left(x,y\right)=\left(3 x^{2},5 y^{4}\right)$$$
$$$\nabla \left(x^{3} + y^{5}\right)|_{\left(x,y\right)=\left(1,7\right)}=\left(3,12005\right)$$$