Example 1: Use the method of taking logarithms to find the derivative y ', if y is given by
y = x sin x
Solution to Example 1
We first note that there is no formula that can be used to differentiate directly this function. The first derivative may be calculated by first taking the natural logarithm of both sides of y = x sin x.
ln y = ln [ x sin x ]
Use logarithm properties to rewrite the above equation as follows