Difference between revisions of "022 Exam 1 Sample A, Problem 8"

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     <td> &nbsp;&nbsp;&nbsp;&nbsp; <math style="vertical-align: -70%">f'(x)</math>&nbsp; </td>
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     <td> &nbsp;&nbsp;&nbsp;&nbsp; <math style="vertical-align: -70%">f'(x)</math>&nbsp;&nbsp; </td>
 
     <td><math>=\,\,\frac{\left[\left(3x-1\right)^{2}\right]'\cdot(x^{3}-7) \,\,-\,\, \left(3x-1\right)^{2}\cdot(x^{3}-7)'}{(x^{3}-7)^{2}}</math></td>
 
     <td><math>=\,\,\frac{\left[\left(3x-1\right)^{2}\right]'\cdot(x^{3}-7) \,\,-\,\, \left(3x-1\right)^{2}\cdot(x^{3}-7)'}{(x^{3}-7)^{2}}</math></td>
 
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     <td></td>
 
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     <td><math>=\frac{\left[2\left(3x-1\right)\cdot3\right]\cdot(x^{3}-7) \,\,-\,\, \left(3x-1\right)^{2}\cdot3x^{2}}{(x^{3}-7)^{2}}.</math></td>
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     <td><math>=\,\,\frac{\left[2\left(3x-1\right)\cdot3\right]\cdot(x^{3}-7) \,\,-\,\, \left(3x-1\right)^{2}\cdot3x^{2}}{(x^{3}-7)^{2}}.</math></td>
 
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Latest revision as of 16:34, 2 April 2015

8. Find the derivative of the function . You do not need to simplify your answer.

Foundations:  
This problem involves some more advanced rules of differentiation. In particular, it requires
The Chain Rule: If and are differentiable functions, then

    

The Quotient Rule: If and are differentiable functions and  , then

    

Solution:  
Note that we need to use chain rule to find the derivative of . Then we find
       


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