SOLUTION: Consider the surface F(x,y,z)=x^6z^2+sin(y^6z^2)−8=0. Find the following partial derivatives ∂z/∂x= Mi answer is -((6xz)/(x^6y^6cos(y^6z^2))) but it's wrong. ∂z/∂y

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Question 1180479: Consider the surface F(x,y,z)=x^6z^2+sin(y^6z^2)−8=0.
Find the following partial derivatives
∂z/∂x=
Mi answer is -((6xz)/(x^6y^6cos(y^6z^2))) but it's wrong.
∂z/∂y=
Mi anwer is -((6y^5zcos(y^6z^2))/(2x^6+2y^6cos(y^6z^2))) it's correct.

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
∂z/∂x= (from WolframAlpha)

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ADDED 5/17
Today I have the time to add the steps, partly for my own benefit:

F(x,y,z) =


Fx = ∂F/∂x =


Fz =


By the Implicit Function Theorem (see https://www.sfu.ca/~wainwrig/Econ331/notes-partials1.pdf)
∂z/∂x = -Fx/Fz =

Canceling a 2z from top and bottom gives:


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