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 $$$f=6 x e^{3}$$$at $$$\left(x,y\right)=\left(2,54\right)$$$
To find the gradient of a function (which is a vector), differentiate the function with respect to each variable.
$$$\nabla f = \left(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y}\right)$$$
$$$\frac{\partial f}{\partial x}=6 e^{3}$$$ (for steps, see derivative calculator)
$$$\frac{\partial f}{\partial y}=0$$$ (for steps, see derivative calculator)
Finally, plug in the point:
$$$\nabla f \left(2,54\right)=\left(6 e^{3},0\right)$$$
Answer
$$$\nabla \left(6 x e^{3}\right) \left(x,y\right)=\left(6 e^{3},0\right)$$$
$$$\nabla \left(6 x e^{3}\right)|_{\left(x,y\right)=\left(2,54\right)}=\left(6 e^{3},0\right)$$$