AP Calc- Derivatives

d/dx [arcsin u]

u’ / sqrt(1-u²)

d/dx [arctan u]

u’ / 1 + u²

d/dx [arcsec u]

u’ / |u| sqrt(1-u²)

d/dx [arcsin (u/a)]

u’ / sqrt(a² - u²)

d/dx [arctan (u/a)]

(a)(u’ ) / a² + u²

d/dx [tan x]

sec² x

d/dx [cot x]

-csc² x

d/dx [sec x]

sec x tan x

csc x

-csc x cot x

d/dx [x² + y² ]

2x + 2y (dy/dx)

d/dx [ xy ]

(1)(y) + (dy/dx) (x)

d/dx [ x² * ln x ]

(2x)(ln x) + (1/x)(x²)

d/dx [ e^x sec x ]

(e^x)(sec x) + (sec x tan x) (e^x)

d/dx [ 3^sqrt(x-2) ]

( (3^sqrt(x-2)) (ln 3) ) (1/(2)(sqrt(x-2)) )

d/dx [ cos^4 (6x) ]

(4(cos³(6x)) (-sin (6x) (6))

d/dx [ f(x) + g(x) ]

f’(x) + g’(x)

d/dx [ f(x) g(x) ]

(f’(x))(g(x)) + (g’(x)) (f(x))

d/dx [ f(x)/g(x) ]

( (f’(x))(g(x)) - (g’(x))(f(x)) ) / g(x)²

d/dx [ f(g(x)) ]

f’(g(x)) (g’(x))

d/dx [ sqrt(x) ]

1 / 2 sqrt(x)