Tricks of the Trade (with Professor Glesser) My all-time
favorite differentiation technique is logarithmic
differentiation. The implementation is right there in the name:
take a logarithm and then differentiate. If you are a pro with
your log rules, you will understand why this would be useful.
There are two canonical types of functions where this technique
is often used in standard calculus courses. The first is where
you have a product and/or quotient of functions, potentially
raised to a rational power. For example: If you apply the
natural log to both sides—we choose base so as to avoid
unnecessary constants when differentiating (recall that when is
a function of that —then we can deconstruct the right hand side
using the log rules to get: Differentiating both sides is now a
snap: Multiplying both sides by —which is the orignal
function—gives us the derivative. The second example is one that
gives students no trouble at all, but gives teachers fits. The
simplest such example is Three-quarters of the class