Differentiate logarithmic functions

The derivative of $\ln x$ is $1/x$ for $x>0$, while the derivative of $\log_a x$ is $1/(x\ln a)$ for $a>0$ and $a\ne1$, reflecting the effect of the logarithm’s base. For compositions such as $\ln(g(x))$ or $\log_a(g(x))$, differentiation uses the chain rule and requires $g(x)>0$; the focus is on explicit functions and standard algebraic combinations, not advanced logarithmic differentiation or more general inverse-function theory.