Question

hi im new to partial differentiation, and im wondering whether im doing it correctly...

Answer 1

Find\[\delta z / \delta r\] when (r,theta) =(2, pi/4) if \[z=4e ^{x} \ln y, x=\ln \left( r \cos \theta \right), y=r \sin \theta\]

Answer 2

the basic chain rule is dz/dr = dz/dx (dx/dr) + dz/dy (dy/dr), d=del
the answer i'd obtained is \[dz/dr = \left( 4e ^{x}*\ln y \right)\left( 1/r \cos \theta \right)+\left( 4e ^{x} *1/y \right)\left( \sin \theta \right)\]

Answer 3

and im not sure when to substitute the (r, theta)=(2, pi/4) into the expression

Answer 4

I would have to study your answer, but just plugging in for x and y
\[ z= 4 r cos\theta ln( r sin \theta ) \]
and then take the derivative wrt r, treating theta as a constant

Answer 5

oo k i try again

Answer 6

oh i got it, tqvm :D