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9) Chain Rule Expertise: So you think you "get" derivatives and the chain rule? Show me. Find the derivative of 3 f(x) = ₁ √1 + x³ sin²(x²) tan(e3r²) In(1 + 2x) HINT: There is an easier way to do it, then there is the "brute- force" way to do it. Think carefully before diving in. (Use logarithmic differentiation).

9) Chain Rule Expertise: So you think you "get" derivatives and the chain rule? Show me. Find the derivative of 3 f(x) = ₁ √1 + x³ sin²(x²) tan(e3r²) In(1 + 2x) HINT: There is an easier way to do it, then there is the "brute- force" way to do it. Think carefully before diving in. (Use logarithmic differentiation).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 47E
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Question 9: Fund the derivative of the following using the chain rule

HINT: It does cross the x-axis, your job is to prove that it does! What does the Intermediate Value Theorem say specifically? CONCEPT CHECK: Without using a calculator, can you find ap- proximately where it crosses the x-axis? Narrow down the domain over which f crosses the x-axis: [a,b]. 9) Chain Rule Expertise: So you think you "get" derivatives and the chain rule? Show me. Find the derivative of f(x) = √1+x³ sin²(x²) tan(e3x²) ln(1 + 2x) HINT: There is an easier way to do it, then there is the "brute- force" way to do it. Think carefully before diving in. (Use logarithmic differentiation). 2
Transcribed Image Text:HINT: It does cross the x-axis, your job is to prove that it does! What does the Intermediate Value Theorem say specifically? CONCEPT CHECK: Without using a calculator, can you find ap- proximately where it crosses the x-axis? Narrow down the domain over which f crosses the x-axis: [a,b]. 9) Chain Rule Expertise: So you think you "get" derivatives and the chain rule? Show me. Find the derivative of f(x) = √1+x³ sin²(x²) tan(e3x²) ln(1 + 2x) HINT: There is an easier way to do it, then there is the "brute- force" way to do it. Think carefully before diving in. (Use logarithmic differentiation). 2
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Did you use the product rule as well? I would like some clarification on the steps.

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