Quick questions on Logarithmic and exponential calculus: derivatives and integrals of e^x and ln(x)

Before differentiating or integrating, simplify with the log laws: $\ln(ab) = \ln a + \ln b$, $\ln(a/b) = \ln a - \ln b$, and $\ln(a^n) = n \ln a$. Rewriting $\ln(x^3)$ as $3 \ln x$ before differentiating turns a chain-rule problem into a one-line answer, $\frac{3}{x}$. Splitting a product or quotient inside a logarithm into a sum or difference of logs is often the fastest route through a derivative.