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Compute the derivatives of the fallowing functions. use any rule but explain what ar methed, did No need to sìnplity. you -1997 Fcn -(sగ) a.fcx)=1+x 2+2x %3D c.tex)=sin(x?-x+1) difex)-sin?x

Compute the derivatives of the fallowing functions. use any rule but explain what ar methed, did No need to sìnplity. you -1997 Fcn -(sగ) a.fcx)=1+x 2+2x %3D c.tex)=sin(x?-x+1) difex)-sin?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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### Derivatives of Functions **Problem:** Compute the derivatives of the following functions. Use any rule or method, but explain what you did. No need to simplify. #### Functions: a. \( f(x) = \frac{1 + x}{x^2 + 2x} \) b. \( f(x) = (\cos x)^{-1997} \) c. \( f(x) = \sin(x^2 - x + 1) \) d. \( f(x) = \sqrt{\sin 3x} \) ### Instructions: 1. For each function, consider which differentiation rules are applicable (e.g., product rule, quotient rule, chain rule). 2. Compute the derivative and briefly explain the steps involved. 3. Simplification of the final answer is not required. This exercise helps in understanding the application of calculus rules to different types of functions.
Transcribed Image Text:### Derivatives of Functions **Problem:** Compute the derivatives of the following functions. Use any rule or method, but explain what you did. No need to simplify. #### Functions: a. \( f(x) = \frac{1 + x}{x^2 + 2x} \) b. \( f(x) = (\cos x)^{-1997} \) c. \( f(x) = \sin(x^2 - x + 1) \) d. \( f(x) = \sqrt{\sin 3x} \) ### Instructions: 1. For each function, consider which differentiation rules are applicable (e.g., product rule, quotient rule, chain rule). 2. Compute the derivative and briefly explain the steps involved. 3. Simplification of the final answer is not required. This exercise helps in understanding the application of calculus rules to different types of functions.
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