022 Exam 1 Sample A, Problem 8 - Revision history

MathAdmin at 23:34, 2 April 2015

2015-04-02T23:34:41Z

MathAdmin at 22:59, 2 April 2015

2015-04-02T22:59:13Z

MathAdmin at 21:02, 2 April 2015

2015-04-02T21:02:25Z

MathAdmin: Created page with "8. Find the derivative of the function $f(x)=\frac{(3x-1)^{2}}{x^{3}-7}$ . You do not need to simplify your..."

2015-04-02T21:01:04Z

Created page with "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..."

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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.

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Foundations:  
|-
|This problem involves some more advanced rules of differentiation. In particular, it requires
|-
|'''The Chain Rule:''' If <math style="vertical-align: -25%;">f</math> and <math style="vertical-align: -15%;">g</math> are differentiable functions, then
|-

|      <math>(f\circ g)'(x) = f'(g(x))\cdot g'(x).</math>
|-
| '''The Quotient Rule:''' If <math style="vertical-align: -25%;">f</math> and <math style="vertical-align: -15%;">g</math> are differentiable functions and <math style="vertical-align: -21%;">g(x) \neq 0</math> , then
|-
|      <math>\left(\frac{f}{g}\right)'(x) = \frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{\left(g(x)\right)^2}. </math>
|-
| 
|}

 '''Solution:'''

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Step 1:  
|-

@@ Line 26: / Line 26: @@
 |<table>
    <tr style="vertical-align: middle">
-     <td> &nbsp;&nbsp;&nbsp;&nbsp; <math style="vertical-align: -70%">f'(x)</math>&nbsp; </td>
+     <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>
+     <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>
 |}

@@ 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;"
@@ Line 18: / Line 18: @@
 |<br>
 |}
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
+!Solution: &nbsp;
 |-
 |}
 [[022_Exam_1_Sample_A|'''<u>Return to Sample Exam</u>''']]

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022 Exam 1 Sample A, Problem 8 - Revision history

MathAdmin at 23:34, 2 April 2015

MathAdmin at 22:59, 2 April 2015

MathAdmin at 21:02, 2 April 2015

MathAdmin: Created page with "8. Find the derivative of the function f(x)=\frac{(3x-1)^{2}}{x^{3}-7}. You do not need to simplify your..."

MathAdmin: Created page with "8. Find the derivative of the function $f(x)=\frac{(3x-1)^{2}}{x^{3}-7}$ . You do not need to simplify your..."