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1. Find the derivative dy/dx for each of the following. Simplify answers. (a) y = (3x* + 2)¯° (b) y = In (e*" + æ) (c) y = x³ In(5x + 3)

1. Find the derivative dy/dx for each of the following. Simplify answers. (a) y = (3x* + 2)¯° (b) y = In (e*" + æ) (c) y = x³ In(5x + 3)

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
## Problem 1: Find the Derivative \( \frac{dy}{dx} \) for Each of the Following. Simplify Answers. ### (a) \( y = (3x^4 + 2)^{-6} \) ### (b) \( y = \ln(e^{4x} + x) \) ### (c) \( y = x^3 \ln(5x + 3) \) --- In this problem, you'll use differentiation techniques such as the chain rule, product rule, and logarithmic differentiation to solve for the derivatives. For part (a), apply the chain rule. Part (b) requires using the derivative of a logarithm, and part (c) utilizes the product rule combined with logarithmic differentiation.
Transcribed Image Text:## Problem 1: Find the Derivative \( \frac{dy}{dx} \) for Each of the Following. Simplify Answers. ### (a) \( y = (3x^4 + 2)^{-6} \) ### (b) \( y = \ln(e^{4x} + x) \) ### (c) \( y = x^3 \ln(5x + 3) \) --- In this problem, you'll use differentiation techniques such as the chain rule, product rule, and logarithmic differentiation to solve for the derivatives. For part (a), apply the chain rule. Part (b) requires using the derivative of a logarithm, and part (c) utilizes the product rule combined with logarithmic differentiation.
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