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

From Math Wiki
Jump to navigation Jump to search
(Created page with "<span style="font-size:135%">8. Find the derivative of the function <math style="vertical-align: -43%">f(x)=\frac{(3x-1)^{2}}{x^{3}-7}</math>. You do not need to simplify your...")
 
m
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
<span style="font-size:135%">8. Find the derivative of the function <math style="vertical-align: -43%">f(x)=\frac{(3x-1)^{2}}{x^{3}-7}</math>.
+
<span style="font-size:135%"><font face=Times Roman>8. Find the derivative of the function <math style="vertical-align: -43%">f(x)=\frac{(3x-1)^{2}}{x^{3}-7}</math>.
You do not need to simplify your answer.
+
You do not need to simplify your answer.</font face=Times Roman>
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
Line 19: Line 19:
 
|}
 
|}
  
 +
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 +
!Solution: &nbsp;
 +
|-
 +
|Note that we need to use chain rule to find the derivative of <math style="vertical-align: -25%;">\left(3x-1\right)^2</math>.  Then we find
 +
|-
 +
|<table>
 +
  <tr style="vertical-align: middle">
 +
    <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>
 +
  </tr>
 +
  <tr>
 +
    <td></td>
 +
    <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>
 +
</table>
 +
|}
  
&nbsp;'''Solution:'''
 
  
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+
[[022_Exam_1_Sample_A|'''<u>Return to Sample Exam</u>''']]
!Step 1: &nbsp;
 
|-
 

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
       


Return to Sample Exam