ap calc formulas

basic rules

100

da/dx

0

200

d/dx(au)

a du/dx

300

d/dx(x^n)

nx^(n-1)

400

d/dx(uv)

(u)dv/dx + (v)du/dx

500

d/dx(u/v)

(v(du/dx)-u(dv/dx))/(v^2)

trig rules

100

d/dx(sin u)

(cos u)du/dx

200

d/dx(cos u)

(-sin u)du/dx

300

d/dx(tan u) 

(sec^2 u)du/dx

400

d/dx(cot u)

(-csc^2 u)du/dx

500

d/dx(sec u)

d/dx(csc u)

(sec u)(tan u)du/dx

(-csc u)(cot u)du/dx

general calc rules

100

d/dx(ln u)

(1/u)du/dx

200

d/dx(e^u)

(e^u)du/dx

300

d/dx(a^u)

(a^u)(ln a)du/dx

400

(f(g(x)))'

f'(g(x))*g'(x)

f'(u)*g'(x)

(dy/du)(du/dx)

500

if y=e^((sinx)+1), find dy/dx

dy/dx = cosx*e^((sinx)+1)

more trig rules

100

d/dx(sin^-1 u)

1/(sqrt(1-(u^2))) du/dx

200

d/dx(cos^-1 u)

-1/(sqrt(1-(u^2))) du/dx

300

d/dx(tan^-1 u) 

1/(1+u^2) du/dx

400

d/dx(cot^-1 u)

-1/(1+u^2) du/dx

500

d/dx(csc^-1 u)

-1/|u|sqrt(u^2-1) du/dx