Answered: Use the Chain Rule to evaluate the…

Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2√2, 4) 1 where g(x, y) = , x = r sin 0, y = r cos 0. 2x+8y²2 8g = |(r,0)=(2√²,7) | 3 100

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

how do i solve this chain rule question?

Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2√2, 4)
where g(x, y) = 2x+8y² » x = r sin 0, y = r cos 0.
8g
|(r,0)=(2√2,7)
=
3
100

Expert Solution

Step 1

Given,

$g (x, y) = \frac{1}{(2 x + 8 y^{2})}, x = r \cos (θ), y = r \sin (θ)$

The Partial Derivative, $\frac{\partial g}{\partial θ}$ is to be found at $(r, θ) = (2 \sqrt{2}, \frac{π}{4}) .$

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