If we first simplify the given function using the laws of logarithms, the differentiation becomes easier
example: Thus, f ’(x) = 1/x for all x ≠ 0. The result is worth remembering:
a logarithmic function with base a in terms of the natural logarithmic function: example:
LOGARITHMIC DIFFERENTIATION 1.Take natural logarithms of both sides of an equation y = f(x) and simplify. 2. Differentiate implicitly with respect to x. 3. Solve the resulting equation for y’. example: differentiate Since we have an explicit expression for y, we can substitute and write If we hadn’t used logarithmic differentiation the resulting calculation would have been horrendous.