Derivatives of Basic Functions

Example:
z = ln(y)

This is just the derivative of a basic function, which we have to remember. These derivatives include the following.

The Derivative of Basic Functions:

  ( e x )' = e x
  ( a x )' = ln(a) a x
  ( sin(x) )' = cos(x)
  ( cos(x) )' = -sin(x)
  ( ln(x) )' = 1 / x
 
  ( tan(x) )' = 1 / ( cos(x) )2
  ( arctan(x) )' = 1 / ( 1 + x2 )
  ( arcsin(x) )' = 1 / sqrt( 1 - x2 )
  ( arccos(x) )' = -1 / sqrt( 1 - x2 )

So our example,

z = ln(y)
Must have one as its derivative
z ' = y-1
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©2001 Gavin LaRose, University of Michigan Math Dept.