Logarithm Derivative Calculator

Three jobs that all go through a logarithm. The first differentiates log_b(u(x)) for a polynomial u and any base, returning u' over u times ln b with the working shown. The second is logarithmic differentiation proper: give a product or quotient of polynomial factors raised to whole powers and it takes logs, differentiates the sum and multiplies back by y. The third handles a variable base raised to a variable power, where neither the power rule nor the exponential rule applies. Each answer is checked against a central difference of the original function, and the check is printed beside it.