Derivative of exponential and logarithmic functions

$e^x$ , $\ln x$ , $a^x$ , $\log_a x$

Standard school tabulation

Function	Derivative (on $D$ )	Remark
$e^x$	$(e^x)'=e^x$	exponential “is its own” derivative
$\ln x$ , $x>0$	$(\ln x)'=\dfrac{1}{x}$	derivative is the hyperbola $y=1/x$ on $(0,+\infty)$
$a^x$ , $a>0$ , $a\neq1$	$(a^x)'=a^x\ln a$	$\ln e=1$ recovers $e^x$
$\log_a x$ , $x>0$	$(\log_a x)'=\dfrac{1}{x\ln a}$	special case when $a=e$

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