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Name: Find the derivativea) f(x) = (x2 - √x ) . exb) g(x) = (x2)/ ( c + xex
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Description: Find the derivativea) f(x) = (x2 - √x ) . exb) g(x) = (x2)/ ( c + xex)

Math

Calculus

Find the derivative a) f(x) = (x2 - √x ) . ex b) g(x) = (x2)/ ( c + xex)

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 3CC: If xis large, which function grows faster, f(x)=2x or g(x)=x2?

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Topic Video

Question

Find the derivative

a) f(x) = (x² - √x ) . e^x

b) g(x) = (x²)/ ( c + xe^x)

Expert Solution

Step 1

A) Find the derivative as shown below:

$f' (\frac{x^{2} - \sqrt{x}}{e^{x}}) = \frac{d}{d x} (\frac{x^{2} - \sqrt{x}}{e^{x}}) = \frac{\frac{d}{d x} (x^{2} - \sqrt{x}) e^{x} - \frac{d}{d x} (e^{x}) (x^{2} - \sqrt{x})}{{(e^{x})}^{2}} = \frac{(2 x - \frac{1}{2 \sqrt{x}}) e^{x} - e^{x} (x^{2} - \sqrt{x})}{{(e^{x})}^{2}} = \frac{- 1 + 4 x \sqrt{x} - 2 x^{2} \sqrt{x} + 2 x}{2 e^{x} \sqrt{x}}$

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