Difference between revisions of "009A Sample Final 3, Problem 2"

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<span class="exam"> Find the derivative of the following functions:
 
<span class="exam"> Find the derivative of the following functions:
  
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<span class="exam">(a) <math>g(\theta)=\frac{\pi^2}{(\sec\theta -\sin 2\theta)^2}</math>
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<span class="exam">(a) &nbsp;<math style="vertical-align: -18px">g(\theta)=\frac{\pi^2}{(\sec\theta -\sin 2\theta)^2}</math>
  
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<span class="exam">(b) <math>y=\cos(3\pi)+\tan^{-1}(\sqrt{x})</math>
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<span class="exam">(b) &nbsp;<math style="vertical-align: -5px">y=\cos(3\pi)+\tan^{-1}(\sqrt{x})</math>
  
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!Foundations: &nbsp;
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[[009A Sample Final 3, Problem 2 Solution|'''<u>Solution</u>''']]
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|'''1.''' '''Chain Rule'''
 
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|&nbsp; &nbsp; &nbsp; &nbsp; <math>\frac{d}{dx}(f(g(x)))=f'(g(x))g'(x)</math>
 
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|'''2.''' '''Trig Derivatives'''
 
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|&nbsp; &nbsp; &nbsp; &nbsp; <math>\frac{d}{dx}(\sin x)=\cos x,\quad\frac{d}{dx}(\sec x)=\sec x \tan x</math>
 
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|'''3.''' '''Inverse Trig Derivatives
 
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|&nbsp; &nbsp; &nbsp; &nbsp; <math>\frac{d}{dx}(\tan^{-1} x)=\frac{1}{1+x^2}</math>
 
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'''Solution:'''
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[[009A Sample Final 3, Problem 2 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
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'''(a)'''
 
  
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!Step 2: &nbsp;
 
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'''(b)'''
 
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'''(c)'''
 
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!Final Answer: &nbsp;
 
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|'''(a)'''
 
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|'''(b)'''
 
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|'''(c)'''
 
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[[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]
 
[[009A_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 16:34, 2 December 2017

Find the derivative of the following functions:

(a)  

(b)  

Solution


Detailed Solution


Return to Sample Exam

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