1linear approximation
$l(x) = f(a)+f'(a)(x-a)
2$\frac{d}{dx} (e^{g(x)})
$e^{g(x)}\times{g'(x)}
3$\frac{d}{dx} (\ln {g(x)})
$\frac{1}{g(x)}\times g'(x)
4$\frac{d}{dx}(b^{g(x)})
$b^{g(x)}\times g'(x) \times \ln b
5$\frac{d}{dx}(log_bg(x))
$\frac{g'(x)}{g(x)lnb}
6If f''(x) > positive over interval I
f is concave up over I
7If f''(x) is negative over interval I
f is concave down over I
8If f'(c)=0 and f''(c) is positive then
f has a local minimum at c
9If f'(c)=0 and f''(c) is negative then
f has a local maximum at c
10If f'(c)=0 and f''(c)=0 then
evaluate at f'(x)
11chain rule
$\frac{d}{dx} f(g(x)) = f'(g(x))g'(x)
15$\ln(\frac{x}{y})$
ln x - ln y
16$\frac{d}{dx} log_bx$
$\frac{1}{x\ln b}$
17$\frac{d}{dx} \sin x
cos x
18$\frac{d}{dx} \tan x
$\sec ^2 x$
19$\frac{d}{dx}sec x
sec x tan x
20$\frac{d}{dx} \cos x
-sin x
21$\frac{d}{dx} \cot x
$-\csc ^2 x
22$\frac{d}{dx} csc x
$-\csc x cot x