Difference between revisions of "009A Sample Midterm 2, Problem 4"

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(Created page with "<span class="exam">Find the derivatives of the following functions. Do not simplify. <span class="exam">(a)   <math style="vertical-align: -5px">f(x)=x^3(x^{\frac{4}{3}}...")
 
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!Final Answer: &nbsp;  
 
!Final Answer: &nbsp;  
 
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|&nbsp; &nbsp; '''(a)''' &nbsp; &nbsp; <math>x^3\bigg(\frac{4}{3}x^{\frac{1}{3}}\bigg)+(3x^2)(x^{\frac{4}{3}}-1)</math>  
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|&nbsp; &nbsp; '''(a)''' &nbsp; &nbsp; <math>f'(x)=x^3\bigg(\frac{4}{3}x^{\frac{1}{3}}\bigg)+(3x^2)(x^{\frac{4}{3}}-1)</math>  
 
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|&nbsp; &nbsp; '''(b)''' &nbsp; &nbsp; <math>\frac{(1+6x)(3x^2-3x^{-4})-(x^3+x^{-3})(6)}{(1+6x)^2}</math>  
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|&nbsp; &nbsp; '''(b)''' &nbsp; &nbsp; <math>g'(x)=\frac{(1+6x)(3x^2-3x^{-4})-(x^3+x^{-3})(6)}{(1+6x)^2}</math>  
 
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[[009A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]
 
[[009A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

Revision as of 19:50, 13 April 2017

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

(a)  

(b)     where  


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


Solution:

(a)

Step 1:  
Using the Product Rule, we have
       
Step 2:  
Now, we have
       

(b)

Step 1:  
Using the Quotient Rule, we have
       
Step 2:  
Now, we have
       


Final Answer:  
    (a)    
    (b)    

Return to Sample Exam