Use implicit differentiation to find ∂z / ∂x and ∂z

Yolanda Jorge

Yolanda Jorge

Answered question

2021-11-11

Use implicit differentiation to find ∂z / ∂x and ∂z / ∂y.
e4z=xyz

Answer & Explanation

Louise Eldridge

Louise Eldridge

Beginner2021-11-12Added 17 answers

Given:
e4z=xyz
Partial differentiating both the sides with respect to x:
ddx(e4z)=ddx(xyz)
e4zdzdx=xydzdx+yz
e4zdzdxxydzdx=yz
dzdx(e4zxy)=yz
dzdx=yze4xxy
Partial differentiating both sides with respect to y:
ddy(e4z)=ddy(xyz)
e4zdzdy=xydzdy+xz
e4zdzdyxydzdy=xz
dzdy(e4zxy)=xz
dzdy=xze4zxy

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