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2. (25 pts.) Differentiate the following a. h(t) = e'(t2 - 2t + 2) b. p(x) = 3x/2 c. y(x) = xcosx + tan(5x) -1 d. g(1) = () 312–1 31+1

2. (25 pts.) Differentiate the following a. h(t) = e'(t2 - 2t + 2) b. p(x) = 3x/2 c. y(x) = xcosx + tan(5x) -1 d. g(1) = () 312–1 31+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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**Problem 2:** *(25 points)* Differentiate the following functions: **a.** \( h(t) = e^{(t^2 - 2t + 2)} \) **b.** \( p(x) = 3x^{\sqrt{2}} \) **c.** \( y(x) = x \cos x + \tan^{-1}(5x) \) **d.** \( g(t) = \left(\frac{3t^2 - 1}{3t^2 + 1}\right)^{-3} \) **e.** \( p(\theta) = \frac{k\theta - \cot \alpha}{A\theta + B} \) These exercises involve applying differential calculus techniques, such as the chain rule, product rule, and quotient rule, to find the derivatives of the given functions.
Transcribed Image Text:**Problem 2:** *(25 points)* Differentiate the following functions: **a.** \( h(t) = e^{(t^2 - 2t + 2)} \) **b.** \( p(x) = 3x^{\sqrt{2}} \) **c.** \( y(x) = x \cos x + \tan^{-1}(5x) \) **d.** \( g(t) = \left(\frac{3t^2 - 1}{3t^2 + 1}\right)^{-3} \) **e.** \( p(\theta) = \frac{k\theta - \cot \alpha}{A\theta + B} \) These exercises involve applying differential calculus techniques, such as the chain rule, product rule, and quotient rule, to find the derivatives of the given functions.
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