calc_tutorial_14_6_025

 
Problem Statement

{7,8,10,11}
{3,5,9,12,13}

Calculate the partial derivative using implicit differentiation.

∂z / ∂x

x2y + 7y2z + xz2 = 12

 
Step 1

Question Sequence

Question 1

Recall the formula for implicit differentiation. Given z defined implicitly as F(x, y, z) = 0 with Fz ≠ 0, then the partial derivative ∂z / ∂x is computed by the following.

∂z / ∂x =

A.
B.
C.
D.

And the partial derivative ∂z / ∂y is computed by the following.

∂z / ∂y =

A.
B.
C.
D.

Thus in order to compute ∂z / ∂x , we need to compute the partial derivatives of F, Fx and Fz.

Find Fx and Fz.

F(x, y, z) = x2y + 7y2z + xz2 − 12 = 0

Fx(x, y, z) =

A.
B.
C.
D.

Fz(x, y, z) =

A.
B.
C.
D.

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

Calculate the partial derivative ∂z / ∂x using implicit differentiation.

∂z / ∂x = − Fx / Fz

A.
B.
C.
D.

Correct.
Incorrect.