Question

Seja a função
h
(
x
,

y
,

z
)

=
(
x
+
2
)
2
l
n

(
y
2
+
z
)
. Determine o vetor gradiente de h(x,y,z)

Answer 1

Resposta:

$h(x,y,z)=(x+2)^{2} ln(y^{2} +z)$

$\frac{\partial h}{\partial x}=2(x+2)ln(y^{2}+z)$

$\frac{\partial h}{\partial y}= \frac{2y(x+2)^{2}}{y^{2}+z }$

$\frac{\partial h}{\partial z} =\frac{(x+2)^{2} }{y^{2}+z }$

$\nabla=\frac{\partial h}{\partial x} I +\frac{\partial h}{\partial y}J+\frac{\partial h}{\partial z}K$

$\nabla=[2(x+2)ln(y^{2}+z)]I+[\frac{2y(x+2)^{2}}{y^{2}+z }]J+[\frac{(x+2)^{2} }{y^{2}+z }]K$

Answer 2

resposta:

$(2(x+2)ln(y2+z),2y(x+2)2y2+z, (x+2)2y2+z)$