Partial Derivatives of z: Find x,y in z(x, y)

[Scottadams92]

Find the two first-order partial derivatives of z with respect to x and y
when z = z(x, y) is defined implicitly by

z*(e^xy+y)+z^3=1.


I started by multiplying the brackets out to give; ze^xy + zy + z^3 - 1 = 0

i then differentiated each side implicitly and got;
dz/dx = yze^xy
and
dz/dy = xze^xy + z

I'm happy with dz/dx but I've gone wrong on the dz/dy and i don't know where.

 

[Mark44]

Find the two first-order partial derivatives of z with respect to x and y
when z = z(x, y) is defined implicitly by

z*(e^xy+y)+z^3=1.


I started by multiplying the brackets out to give; ze^xy + zy + z^3 - 1 = 0

i then differentiated each side implicitly and got;
dz/dx = yze^xy
and
dz/dy = xze^xy + z

I'm happy with dz/dx but I've gone wrong on the dz/dy and i don't know where.

Show us what you got for $\frac{\partial z}{\partial y}$

I suspect that when you differentiated zy you neglected to use the product rule, or when you differentiated z³, you didn't use the chain rule.