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Introduction to Derivatives

Problems for "Techniques of differentiation"

Techniques of Differentiation

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Problem : Find f'(x) for f (x) = 3x 2 + sin(x)


f'(x) = 6x + cos(x)

Problem : Find f'(x) for f (x) = - 4

x =    

Problem : Find f'(x) for f (x) =


  =  
    =  

Problem : Find f'(x) for f (x) = cos(x 2) .


-2x sin(x 2)

Problem : Find f'(x) for f (x) = cos2(x 3) .


Since this is actually a composite of three functions, the chain rule has to be used twice:

(2 cos(x 3))(- sin(x 3))(3x 2) = - 6x 2cos(x 3)sin(x 3)    

Problem : Find the slope of the graph of 4x 2 y = 2y + x at the point (0,0).


Here, implicit differentiation must be used.


42xy + x 2   = 2 + 1  
8xy - 1   = (2 - 4x 2)  
  =  
At (x, y)   = (0, 0),  
  = -  

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