Chapter 1. calc_tutorial_14_5_006

1.1 Problem Statement

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

Calculate the gradient.

1.2 Step 1

Question Sequence

Question 1.1

In two variables, the gradient of a function, f(x, y), is the vector f(x, y) = fx(x, y), fy(x, y). Thus in order to calculate the gradient, we must calculate the first-order derivatives.

Find gx(x, y) and gy(x, y). Note that gx(x, y) requires the quotient rule, but gy(x, y) only requires the chain rule, since the numerator is considered constant.

gx(x, y) = (∂/∂x)($ax/($bx2 + $cy2)) =

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

gy(x, y) = (∂/∂y)($ax/($bx2 + $cy2)) = $ax(∂/∂y)(1/($bx2 + $cy2)) =

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

Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Using the first-order derivatives found in step 1, calculate the gradient vector.

g(x, y) = <gx(x, y), gy(x, y)> =

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

Correct.
Incorrect.