Chapter 1. calc_tutorial_14_3_057

1.1 Problem Statement

{5,6,7}
{2,3,4}
2*$a
4*$b
3*$d

Compute the derivatives indicated.

f(x, y) = $ax2y - $bxy4, ∂2f / ∂x2, ∂2f / ∂y2

1.2 Step 1

Question Sequence

Question 1.1

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 OoQWwj+vEeo= constant.

f / ∂x =

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

Find ∂f / ∂y holding DB8eX8yodOo= constant.

f / ∂y =

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
Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

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 ($cxy − $by4) =

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

2f / ∂y2 = ∂ / ∂y (∂f / ∂y) = ∂ / ∂y ($ax2 − $dxy3) =

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
Incorrect. Do you see where you went wrong?
Excellent work.