AP Calculus AB chain rule/derivatives essentials

what is the chain rule

“the derivative of the outside, keep the inside, times the derivative of the inside”

d/dx sinx

cosx

d/dx tanx

sec²x

d/dx secx

secxtanx

d/dx cosx

-sinx

d/dx cotx

-csc²x

d/dx cscx

-cscxcotx

d/dx lnu

(u’/u)

d/dx log_au

d/dx u’/lna x u

d/dx a^u

lna x a^u x u’

d/dx e^u

e^u x u’

to be differentiable..

function must be continuous as well as its derivative and smooth (no cusps, va or discontinuities)