Chain rule for several variables: Implicit diff.

[soe236]

Homework Statement

Z is defined implicitly as a function of x,y by equation (z^2)x + 3xy^2 + e^((y^2)z) = 4. Find dz/dx

Homework Equations

dz/dx = -Fx/Fz

The Attempt at a Solution

Fx= z^2 + 3y^2
Fz=2zx+(y^2)e^((y^2)z)
dz/dx= (z^2+3y^2)/[2zx+(y^2)e^((y^2)z)]

I'm not sure if I used the partial derivatives correctly, and a little unsure about the procedure as well. Someone please check that and tell me if it's correct. Thankyou

 

[tiny-tim]

(z^2)x + 3xy^2 + e^((y^2)z) = 4. Find dz/dx
…
Fx= z^2 + 3y^2
Fz=2zx+(y^2)e^((y^2)z)
dz/dx= (z^2+3y^2)/[2zx+(y^2)e^((y^2)z)]

Hi soe236!

Looks good to me.

 

[soe236]

Thank you!