Calculating derivatives

We rarely calculate derivatives from their definition. Instead, we rely on a number of rules, summarized below:

Rule Name	Function	Derivative
Power Rule	$x^n, n \text{ a real number.}$	$nx^{n-1}$
Constant Rule	$k$	0
Constant Multiple Rule	$kf(x), k \text{ a constant number.}$	$kf´(x)$
Sum/Difference Rule	$f(x)\pm g(x)$	$f'(x)\pm g'(x)$
Product Rule	$f(x)g(x)$	$f'(x)g(x)+g'(x)f(x)$
Quotient Rule	$\frac{f(x)}{g(x)}$	$\frac{f'(x)g(x)-g'(x)f(x)}{g^2(x)}$

Some rules for specific functions, which sometimes appear in practice:

Function	Derivative
$e^x$	$e^x$
$\ln(x)$	$1/x$
$\sin(x)$	$\cos(x)$
$\cos(x)$	$-\sin(x)$
$\tan(x)$	$\sec^2(x)$