Derivative rules

0.	slope of tangent	$\displaystyle f'(a)=\lim_{b\to a}{{f(b)-f(a)}\over {b-a}}$	$\displaystyle f'(x)=\lim_{h\to 0}{{f(x+h)-f(x)}\over h}$
1.	sum	(f+g)'=f'+g'
2.	difference	(f-g)'=f'-g'
3.	constant multiple	(cf)'=cf'
4.	product	(fg)'=f'g+fg'
5.	quotient	$\displaystyle\left({f\over g}\right)'={{f'g-fg'}\over {g^2}}$
6.	composition (chain)	$(f\circ g)'=(f'\circ g)g'$	$\displaystyle{{d\over {dx}}}f(g(x))=f'(g(x))g'(x)$
7.	inverse	$\displaystyle(f^{-1})'={1\over {f'\circ f^{-1}}}$	$\displaystyle{{d\over {dx}}}f^{-1}(x)={1\over {f'(f^{-1}(x))}}$
8.	constant		$\displaystyle{{d\over {dx}}}c=0$
9.	power		$\displaystyle{{d\over {dx}}}x^n=nx^{n-1}$
10.	exponent		$\displaystyle{{d\over {dx}}}a^x=a^x\ln a$
11.			$\displaystyle{{d\over {dx}}}e^x=e^x$
12.	logarithm		$\displaystyle{{d\over {dx}}}\log_bx={1\over {x\ln b}}$ restricted to $(0,\infty )$
13.			$\displaystyle{{d\over {dx}}}\ln x={1\over x}$ restricted to $(0,\infty )$
14.	sin	$\sin'=\cos$	$\displaystyle{{d\over {dx}}}\sin(x)=\cos(x)$
15.	cos	$\cos'=-\sin$
16.	tan	$\displaystyle\tan'={1\over {\cos^2}}$	$\displaystyle{{d\over {dx}}}\tan(x)={1\over {\cos^2(x)}}$
17.	arcsin		$\displaystyle{{d\over {dx}}}\arcsin(x)={1\over {\root \of {1-x^2}}}$
18.	arccos		$\displaystyle{{d\over {dx}}}\arccos(x)=-{1\over {\root \of {1-x^2}}}$
19.	arctan		$\displaystyle{{d\over {dx}}}\arctan(x)={1\over {1+x^2}}$