Calc AB Unit 3 Derivative Properties

d/dx [c]

0

d/dx [cu]

cu’

d/dx [uⁿ]

nu^n-1(u’)

d/dx [u±v]

u’ ± v’

d/dx [uv]

uv’ + vu’

d/dx [u/v]

vu’ - uv’ / v²

d/dx e^u

e^u u’

d/dx ln u

u’/u = 1/u * u’

d/dx [sin u]

(cosu)u’ = u’cosu

d/dx [cos u]

(-sinu)u’ = -u’sinu

d/dx [tan u]

(sec²u)u’ = u’sec²u

d/dx [sec u]

(secutanu)u’ = u’secutanu

d/dx [csc u]

(-cscucotu)u’

d/dx [cot u]

(-csc²u)u’ = -u’csc²u

d/dx a^u

(lna)a^uu’ = u’(lna)a^u

d/dx log_au

lnu/lna = u’/(lna)u

d/dx [arc sin u]

u’/√1-u² ,|u|<1

d/dx [arc cos u]

-u’/√1-u² ,|u|<1

d/dx [arc tan u]

u’/1+u²

d/dx [arc sec u]

u’/|u|√u²-1 ,|u|>1

d/dx [arc csc u]

-u’/|u|√u²-1 ,|u|>1

d/dx [arc cot u]

-u’/1+u²