Difference between revisions of "009A Sample Midterm 3, Problem 5"

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|'''1.''' Quotient Rule
 
|'''1.''' Quotient Rule
 
|-
 
|-
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|'''2.''' Power Rule
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|'''2.''' Product Rule
 +
|-
 +
|'''3.''' Power Rule
 
|}
 
|}
  
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!Step 1:    
 
!Step 1:    
 
|-
 
|-
−
|
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|Using the Quotient Rule, we have
 
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|-
−
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|&nbsp; &nbsp; &nbsp; &nbsp; <math>f'(x)=\frac{x^{\frac{4}{5}}((3x-5)(-x^{-2}+4x))'-(3x-5)(-x^{-2}+4x)(x^{\frac{4}{5}})'}{(x^{\frac{4}{5}})^2}.</math>
 
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Revision as of 15:31, 17 February 2017

Find the derivatives of the following functions. Do not simplify.

a)Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=\frac{(3x-5)(-x^{-2}+4x)}{x^{\frac{4}{5}}}}
b)Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g(x)=\sqrt{x}+\frac{1}{\sqrt{x}}+\sqrt{\pi}} for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x>0.}


Foundations:  
1. Quotient Rule
2. Product Rule
3. Power Rule


Solution:

(a)

Step 1:  
Using the Quotient Rule, we have
        Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f'(x)=\frac{x^{\frac{4}{5}}((3x-5)(-x^{-2}+4x))'-(3x-5)(-x^{-2}+4x)(x^{\frac{4}{5}})'}{(x^{\frac{4}{5}})^2}.}
Step 2:  

(b)

Step 1:  
Step 2:  


Final Answer:  
(a)
(b)

Return to Sample Exam

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