Differentiation of Logarithmic and Exponential Functions

  • The function y = f(x) = ax is called the exponential function with positive base, or a >1.
  • The domain of an exponential function is the set of all real numbers.
  • The range of the exponential function is the set of all positive real numbers.
  • The derivative of ax with respect to x = ax loga, a>0, a is not equal to 1.
  • Natural exponential function is denoted by y = ex.
  • For real numbers b >1; if bx = a, then logarithm of a to the base b is x.
  • Thus,  logb a = x   if   bx  =  a.
  • The derivative of loga x with respect to x = 1/ x loga, x>0, a>0, a is not equal to 1.
  • To differentiate the functions of the type y=uv, where u and v are the functions of x, first take logarithm of both sides then differentiate with respect to x.
  • The domain of log function is R+. The range of log function is the set of all real numbers.

       Keywords: Derivatives of Logarithmic and Exponential Functions, Logarithmic Differentiation

 

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