AP Calculus Unit 2

derivative at the point x = c (IROC)

lim h—0 ( f(c+h)-f( c) )/h

lim x —c ( f(x) - f( c) )/c

derivative as a function (IROC)

lim h —0 ( f(x+h) - f(x) )/h

d/dx [c]

0

d/dx [c times u]

c times u’

d/dx [x]

1

d/dx [x^n]

nx^(n-1)

d/dx [u +- v]

u’ +- v’

d/x [u times v']

uv’ + vu’

d/dx [u/v]

(vu’ - uv’)/v²

( lo di high - hi di low )/low squared

d/dx [ e^x]

e^x

d/dx [ ln x]

1/x

d/dx [sin x]

cos x

d/dx [ cos x]

-sin x

d/dx [csc x]

-csc x cot x

d/dx cot x

-csc²x

d/dx sec x

sec x tan x

d/dx [tan x]

sec²x

slope of secant line (nm)

AROC: f(b)-f(a) / b - a

equation of a line (nm)

y-y1 = m(x—x1)

normal line

negative reciprocal of normal line slope

differentiable

1. continuous at x = c

2. lim x—c from left = lim x—c from right

non differentiable (nm)

discontinuous

Sharp corner

vertical tangent line