Log Diff Rules. D dx ab 0 this is a constant d dx xn nxn 1 power rule d dx ax axlna derivative of an exponential function d dx xx xx 1 lnx logarithmic differentiation d d x a b 0 this is a constant d d x x n n x n 1 power rule d d x a x a x ln. Log b x y y log b x for example.
The following problems illustrate the process of logarithmic differentiation. Displaystyle frac f f quad implies quad f f cdot the technique is often performed in cases where it is easier to differentiate the logarithm of a function rather than the function itself. Derivative of a log of a function derivative of logs with base other than e first let s look at a graph of the log function with base e that is.
Log 10 3 7 log 10 3 log 10 7 logarithm power rule.
Derivative of a log of a function derivative of logs with base other than e first let s look at a graph of the log function with base e that is. The logarithm of x raised to the power of y is y times the logarithm of x. For example in the problems that follow you will be asked to differentiate expressions where a variable is raised to a. The logarithm of the ratio of two quantities is the logarithm of the numerator minus the logarithm of the denominator.
