Q1.1 dy Find in each case. Simplify as much as possible. You must show all your work. da a) y = cos² (a) + 3+ sin²(x) (b) m(x) = In IG (c) f(x) = loga 1 - cos(x) 1 + cos(x) (2)] a³x²+x ea √r . For this part assume . Assume a > 0, 1. d dx (In(x)) X
Q1.1 dy Find in each case. Simplify as much as possible. You must show all your work. da a) y = cos² (a) + 3+ sin²(x) (b) m(x) = In IG (c) f(x) = loga 1 - cos(x) 1 + cos(x) (2)] a³x²+x ea √r . For this part assume . Assume a > 0, 1. d dx (In(x)) X
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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![**Q1**
**Q1.1**
Find \(\frac{dy}{dx}\) in each case. Simplify as much as possible. You must show all your work.
**a)** \( y = \sqrt[3]{\cos^2(x) + 3 + \sin^2(x)} \)
**b)** \( m(x) = \ln \left[ \left( \frac{1 - \cos(x)}{1 + \cos(x)} \right)^4 \right] \). For this part assume \(\frac{d}{dx}(\ln(x)) = \frac{1}{x}\).
**c)** \( f(x) = \log_a \left[ \frac{a^{3x^2 + x} \cdot a^{\sqrt{x}}}{e^a} \right] \). Assume \( a > 0, a \neq 1 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2cc04b1e-803c-4d9d-b550-d2ae04bcc2b3%2F705130c1-64cd-4c71-8e19-681b54ea1da2%2Fk7qsi3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Q1**
**Q1.1**
Find \(\frac{dy}{dx}\) in each case. Simplify as much as possible. You must show all your work.
**a)** \( y = \sqrt[3]{\cos^2(x) + 3 + \sin^2(x)} \)
**b)** \( m(x) = \ln \left[ \left( \frac{1 - \cos(x)}{1 + \cos(x)} \right)^4 \right] \). For this part assume \(\frac{d}{dx}(\ln(x)) = \frac{1}{x}\).
**c)** \( f(x) = \log_a \left[ \frac{a^{3x^2 + x} \cdot a^{\sqrt{x}}}{e^a} \right] \). Assume \( a > 0, a \neq 1 \).
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