Difference between revisions of "009A Sample Midterm 2, Problem 5"

From Grad Wiki
Jump to navigation Jump to search
 
(8 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
<span class="exam">Find the derivatives of the following functions. Do not simplify.  
 
<span class="exam">Find the derivatives of the following functions. Do not simplify.  
  
::<span class="exam">a) <math>f(x)=\tan^3(7x^2+5) </math>
+
<span class="exam">(a) &nbsp; <math style="vertical-align: -5px">f(x)=\tan^3(7x^2+5) </math>
::<span class="exam">b) <math>g(x)=\sin(\cos(e^x)) </math>
 
::<span class="exam">c) <math>h(x)=\frac{(5x^2+7x)^3}{\ln(x^2+1)} </math>
 
  
 +
<span class="exam">(b) &nbsp; <math style="vertical-align: -5px">g(x)=\sin(\cos(e^x)) </math>
  
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+
<span class="exam">(c) &nbsp; <math style="vertical-align: -18px">h(x)=\frac{(5x^2+7x)^3}{\ln(x^2+1)} </math>
!Foundations: &nbsp;
+
<hr>
|-
+
[[009A Sample Midterm 2, Problem 5 Solution|'''<u>Solution</u>''']]
|'''1.''' Chain Rule
 
|-
 
|'''2.''' Derivatives of trig/ln
 
|-
 
|'''3.''' Quotient Rule
 
|}
 
  
  
'''Solution:'''
+
[[009A Sample Midterm 2, Problem 5 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
'''(a)'''
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Step 1: &nbsp;
 
|-
 
|First, we use the Chain Rule to get
 
|-
 
|&nbsp; &nbsp; &nbsp; &nbsp; <math>f'(x)=3\tan^2(
 
|}
 
  
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Step 2: &nbsp;
 
|-
 
|
 
|-
 
|
 
|}
 
 
'''(b)'''
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Step 1: &nbsp;
 
|-
 
|
 
|-
 
|
 
|-
 
|
 
|-
 
|
 
|}
 
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Step 2: &nbsp;
 
|-
 
|
 
|-
 
|
 
|-
 
|
 
|-
 
|
 
|}
 
 
'''(c)'''
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Step 1: &nbsp;
 
|-
 
|
 
|-
 
|
 
|-
 
|
 
|-
 
|
 
|}
 
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Step 2: &nbsp;
 
|-
 
|
 
|-
 
|
 
|-
 
|
 
|-
 
|
 
|}
 
 
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Final Answer: &nbsp;
 
|-
 
|'''(a)'''
 
|-
 
|'''(b)'''
 
|-
 
|'''(c)'''
 
|}
 
 
[[009A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]
 
[[009A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 15:40, 9 November 2017

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

(a)  

(b)  

(c)  


Solution


Detailed Solution


Return to Sample Exam