# 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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