Logarithmic differentiation ($\frac{d}{dx}\log |f(x)|=f^{\prime }(x)/f(x)$)

Apply the chain rule to the logarithm of a differentiable nonzero real-valued function. This converts products into sums and powers into multiplicative coefficients. In particular, for positive $f=C{\prod }_i{x}_i^{a_i}$, $df/f={\sum }_i{a}_{i}d{x}_i/x_i$. It is useful for monomial uncertainty propagation and for finding relative rates of change.