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2. Let a and b be constant. Applying the chain rule to find the derivative of the following functions. Use correct notations; otherwise points will be deducted. (a) f(x) = (5 — 3x+x²)7 (b) y = 7 sin(2x) + 5 cos²(x)

2. Let a and b be constant. Applying the chain rule to find the derivative of the following functions. Use correct notations; otherwise points will be deducted. (a) f(x) = (5 — 3x+x²)7 (b) y = 7 sin(2x) + 5 cos²(x)

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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Question
Let a and b be constant. Applying the chain rule to find the derivative of the following functions. Use correct notations; otherwise points will be deducted. (a) ƒ(x) = (5 − 3x + x²)² 2. (b) y = 7 sin(2x) + 5 cos²(x)
Transcribed Image Text:Let a and b be constant. Applying the chain rule to find the derivative of the following functions. Use correct notations; otherwise points will be deducted. (a) ƒ(x) = (5 − 3x + x²)² 2. (b) y = 7 sin(2x) + 5 cos²(x)
Expert Solution
Step 1: Concept

The chain rule states that the derivative of f(g(x)) is f'(g(x))g'(x). Essentially this means taking the derivative of the outside function and then multiplying by the derivative of the inside function. For instance, the derivative of sin( 5 x) is cos( 5 x)* 5.

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