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Problems for "Techniques of differentiation"

Problems for "Techniques of differentiation"

Problems for "Techniques of differentiation"

Problems for "Techniques of differentiation"

Problems for "Techniques of differentiation"

Problems for "Techniques of differentiation"

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),  
  = -