Show all work, thank you! Part a, b, and c of question. 2. Differentiate the following, then simplify.a) $ y = \frac{e^{2x} - e^x}{e^x} $b) $ y = \frac{3}{-2x^2} $c) Find the inputs that generate a horizontal tangent line.\[ y = \frac{x^2}{x-1} \]

Answered: 2. Differentiate the following, then…

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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Show all work, thank you! Part a, b, and c of question.

2. Differentiate the following, then simplify.

a) $ y = \frac{e^{2x} - e^x}{e^x} $

b) $ y = \frac{3}{-2x^2} $

c) Find the inputs that generate a horizontal tangent line.

\[ y = \frac{x^2}{x-1} \]

Expert Solution

Step 1: Part(a)

$y equals fraction numerator e to the power of 2 x end exponent minus e to the power of x over denominator e to the power of x end fraction y equals fraction numerator e to the power of x open parentheses e to the power of x minus 1 close parentheses over denominator e to the power of x end fraction y equals e to the power of x minus 1$

Take derivative.

$y apostrophe equals fraction numerator d over denominator d x end fraction open parentheses e to the power of x minus 1 close parentheses y apostrophe equals fraction numerator d over denominator d x end fraction open parentheses e to the power of x close parentheses minus fraction numerator d over denominator d x end fraction open parentheses 1 close parentheses y apostrophe equals e to the power of x minus 0 y apostrophe equals e to the power of x$