Differentiation of Exponential and Logarithmic Functions

In mathematics, the exponential function is a relation of the form y = ax, with the independent variable x ranging over the entire real number line as the exponent of a positive number a. A logarithm, on the other hand, is the exponent or power to which a base must be raised to yield a given number. Exponential functions are an extremely important mathematical concept; they can help to model population growth or even radioactive decay. Logarithmic functions are also extremely useful, especially in helping to rescale large numbers. This owes to their particular utility in helping to rewrite complicated expressions. Being able to calculate the derivatives of these common functions is an essential part of understanding calculus.