Skip to content

Mathematics · Ch 18 — Differentiation

Derivatives of Logarithmic and Exponential Functions

18.2.7

Derivatives of Logarithmic and Exponential Functions

A reference table of logarithmic and exponential derivatives:

y=f(x)dy/dx=f′(x)log⁡x1/xexexaxaxlog⁡a\begin{array}{ll}y=f(x) & dy/dx=f'(x)\\ \hline \log x & 1/x\\ e^x & e^x\\ a^x & a^x\log a\end{array}

All three were proved by first principles in section 9.1.4 (log⁡x\log x and axa^x directly; exe^x as the 'Try the following' companion exercise, being the special case a=ea=e of axa^x, since log⁡e=1\log e=1). Together with Tables 9.2.5 and 9.2.6, this com …

Table 1Table 9.2.7 — logarithmic and exponential function derivatives

y = f(x) -> dy/dx = f'(x)

log x -> 1/x

e^x -> e^x …

Start your 14-day free trial to unlock the full solution →
← Previous · 18.2.6Derivatives of Trigonometric FunctionsNext · 18.2.8 →Brief Idea of L'Hospital's Rule