Consider the surface F(x,y,z)=x5z2+sin(y4z2)−10=0.

Question

Consider the surface F(x,y,z)=x5z2+sin(y4z2)−10=0.

Find the following partial derivatives

∂z∂x=

∂z∂y=

Answer 1

∂ z / ∂ x = - [ ∂ F / ∂ x ] / [ ∂ F / ∂ z ] = − [ 5 x⁴ z² ] / [ 2 x⁵ z + 2 z y⁴ cos ( y⁴ z² )]

∂ z / ∂ y = - [ ∂ F / ∂ y ] / [ ∂ F / ∂ z ] = − [ 4 y³ z² cos ( y⁴ z² ) ] / [ 2 x⁵ z + 2 z y⁴ cos ( y⁴ z² )]