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2. (a) Let z ry, r =r cost and y=r sin t. Compute by using the chain rule and express your answer in terms of r and t. Let f(r, y)= +2ry. Find the maximum directional derivative (b) of f(r, y) at (1,-1).

2. (a) Let z ry, r =r cost and y=r sin t. Compute by using the chain rule and express your answer in terms of r and t. Let f(r, y)= +2ry. Find the maximum directional derivative (b) of f(r, y) at (1,-1).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Sure! Here is the transcribed text suitable for an educational website: --- ### Problem 2 #### (a) Let \( z = xy^2 \), \( x = r \cos t \), and \( y = r \sin t \). Compute \(\frac{dz}{dt}\) by using the chain rule and express your answer in terms of \( r \) and \( t \). #### (b) Let \( f(x, y) = x^2 + 2xy \). Find the maximum directional derivative of \( f(x, y) \) at \( (1, -1) \). --- Feel free to ask if you need further explanations or solutions for these problems!
Transcribed Image Text:Sure! Here is the transcribed text suitable for an educational website: --- ### Problem 2 #### (a) Let \( z = xy^2 \), \( x = r \cos t \), and \( y = r \sin t \). Compute \(\frac{dz}{dt}\) by using the chain rule and express your answer in terms of \( r \) and \( t \). #### (b) Let \( f(x, y) = x^2 + 2xy \). Find the maximum directional derivative of \( f(x, y) \) at \( (1, -1) \). --- Feel free to ask if you need further explanations or solutions for these problems!
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