calc_tutorial_14_3_057

 
Problem Statement

{5,6,7}
{2,3,4}
2*7
4*3
3*12

Compute the derivatives indicated.

f(x, y) = 7x2y - 3xy4, ∂2f / ∂x2, ∂2f / ∂y2

 
Step 1

Question Sequence

Question 1

In order to compute the second-order derivatives ∂2f / ∂x2 and ∂2f / ∂y2, we need to first compute the first-order derivatives.

Find ∂f / ∂x holding constant.

∂f / ∂x =

A.
B.
C.
D.

Find ∂f / ∂y holding constant.

∂f / ∂y =

A.
B.
C.
D.
Correct.
Incorrect.

 
Step 2

Question Sequence

Question 2

Using the first-order derivatives, compute the second-order derivatives ∂2f / ∂x2 and ∂2f / ∂y2 holding the appropriate variable as a constant.

∂2f / ∂x2 = ∂ / ∂x (∂f / ∂x) = ∂ / ∂x (14xy − 3y4) =

A.
B.
C.
D.

∂2f / ∂y2 = ∂ / ∂y (∂f / ∂y) = ∂ / ∂y (7x2 − 12xy3) =

A.
B.
C.
D.
Incorrect. Do you see where you went wrong?
Excellent work.