AP Calculus AB Unit 2: Derivative Rules and Definitions

d/dx[sinx]

cosx

d/dx[cosx]

-sinx

d/dx[tanx]

sec^2x

d/dx[secx]

secxtanx

d/dx[cotx]

-csc^2x

d/dx[cscx]

-cscxcotx

Trick to memorize

sec(x)sec(x)tan(x) and -csc(x)csc(x)cot(x)

Limit Definition

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

Alternate Form

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

Derivative at a point

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

Slope equation

y-y1=m(x-x1)

If f is differentiable (function has derivative at point) at x=c,

then f is continuous at x=c

Not differentiable

1) Any discontinuity

2) Corner or cusp (sharp turn)

3) Vertical tangent line

Constant rule

d/dx [c] = 0

d/dx [lnx]

1/x

sin(0)

0

cos(0)

1

tan(0)

0

sin(pi/2)

1

Cos(pi/2)

-1

Derivative of arcsin(x)