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