unit 2 ap calc

power rule

y=cx^n y’=ncx^(n-1)

product rule

y’=fg’ + gf’

quotient rule

(gf’-fg’)/(g²)

chain rule

f’(g(x))g’

y=sin(u)

y’=acos(u)

y=cos(u)

y’=-asin(u)

y=tan(u)

y’=asec²x

y=csc(u)

y’=-acotxcscx

y=sec(u)

y’=asecxtanx

y=cot(u)

y’=acsc²x

differential definition

f’(x)=lim f(x+h)-f(x)

h>0 h

distances formula

((x-x)²+(y-y)²)^1/2

arcsin(u)

1/(1-u²)^1/2

arccos(u)

-1/(1-u²)^1/2

arctan(u)

1/(1+u²)