Find (partial derivatives) dz/dv, if z= x^2 + xy^3 where x = uv^2 + w^3
and y = u + ve^w, u = 2, v=1, w=0

Question

Find (partial derivatives) dz/dv, if z= x^2 + xy^3 where x = uv^2 + w^3
and y = u + ve^w,  u = 2, v=1, w=0

ganeshie8 · Answer

$\large \frac{\partial z}{\partial v} = \frac{\partial z}{\partial x} \frac{\partial x}{\partial v} +\frac{\partial z}{\partial y} \frac{\partial y}{\partial v}  $

ganeshie8 · Answer

find partials of z, with respect to x and y 
find partials fo x and y with respect to v
plugin

anonymous · Answer

can you show me working out plz?

ganeshie8 · Answer

$\large  z = x^2 + xy^3$

$\large  \frac{\partial z}{\partial x}  = 2x + y^3$

$\large  \frac{\partial z}{\partial y}  = 3xy^2$

ganeshie8 · Answer

$\large  x = uv^2 + w^3 $
$\large y = u + ve^w $ 

$\large   \frac{\partial x}{\partial v}  = 2uv$

$\large   \frac{\partial y}{\partial v}  = e^w$

ganeshie8 · Answer

plug them

mathmale · Answer

attachment

mathmale · Answer

@bizpro:  I found it easier to write out a solution on paper.  See the attached image.  Please ask all the questions you want.  MM

anonymous · Answer

thnx :)