AP Calculus Unit 2

AP Calculus

Definition of derivative

lim h->0 f(x+h)-f(x)/h

Derivative at a point

lim x->c f(x)-f(c)/x-c

Alternate Form of the Derivative

f'(c) = lim x->c (f(x)-f(c))/(x-c)

Equation of the tangent line

y-f(a) = f'(a)(x-a)

Derivative Power Rule

d/dx x^n = nx^n-1

Sinθ

opposite/hypotenuse

Cosθ

adjacent/hypotenuse

Tanθ

Opposite/Adjacent

π/3

(1/2,√3/2)

π/4

(√2/2,√2/2)

π/6

(√3/2,1/2)

π

(-1,0)

0

(1,0)

cosecantθ

1/sinθ

secantθ

1/cosθ

cotanθ

cosθ/sinθ

y’[tan x]

sec²x

y’[sec x]

secx tanx

y’[cot x]

-csc²x

y’[csc]

-cscxcotx

csc²x

1+cot²x

sec²x

tan²x+1