Chapter 1. calc_tutorial_14_3_022

1.1 Problem Statement

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

Compute the partial derivatives.

1.2 Step 1

Since z is a function of only u and v, the first-order partial derivatives we desire are ∂z / ∂u and ∂z / ∂v.

Question Sequence

Question 1.1

Since z is a composition of functions, these derivatives will require the 6a2baTedFr6uEsDexPkWPq20bF9V2/liqEwcYg== rule.

Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Compute ∂z / ∂u by holding 8UYTXmTWLQs= constant.

z / ∂u = (∂ / ∂u)$a sin($bu2v) = $a cos($bu2v)(∂ / ∂u)($bu2v) =

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

1.4 Step 3

Question Sequence

Question 1.3

Compute ∂z / ∂v by holding CRL4zgGmd/0= constant.

z / ∂v = (∂ / ∂v)$a sin($bu2v) = $a cos($bu2v)(∂ / ∂v)($bu2v) =

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