Higher order derivatives

Lessons

• Introduction
  The concept of higher order derivatives
  

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• 1.
  $1^{st}$ and $2^{nd}$ derivatives.
  Find the first and second derivative for the following functions:
  
  a)

  $f(x)=x^4+5x^2+3x+2$
  
  
  b)

  $f(t)=\sin (2t)$
  
  
  c)

  $g(s)=(2s+5s^2)^7$
  
  
  d)

  $y=5$
  
  
  e)

  $f(x)=5 \ln x$
  
  

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• 2.
  $2^{nd}$ derivatives with implicit differentation
  Find $y"$ by implicit differentiation for the following functions:
  
  a)

  $x^2+y^2=9$
  
  
  b)

  $x^2+xy=9$
  
  

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• 3.
  Derivatives with repeating patterns
  Find $f^{(100)}(x)$ for the following functions:
  
  a)

  $f(x)= \sin (x)$
  
  
  b)

  $f(x)=e^{(2x)}$
  
  

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