Calculus - Unit 3 Rules

d/dx (sin x) =

cos x d/dx

d/dx (cos x) =

-sin x d/dx

d/dx (tan x) =

sec^2 x d/dx

d/dx (csc x) =

-csc x cot x d/dx

d/dx (sec x) =

sec x tan x d/dx

d/dx (cot x) =

-csc^2 x d/dx

f'(x) in limit form

lim h->0 ( f(x+h) - f (x) ) / h

f'(x) at a point

lim x->a ( f(x) - f(a) ) / x-a

Constant function

d/dx (c) = 0

Power rules

d/dx(x^n) = nx^(n-1)

Constant Multiple Rule

d/dx (cu) = c du/dx

Sum Rule & Difference Rules

(u +- v)' = u' +- v'

Product Rule

d/dx (uv) = uv' + vu'

Quotient Rule

d/dx (u/v) = (vu' - uv')/v²

Chain Rule

d/dx f(g(x)) = f'(g(x)) g'(x)

Power Chain Rule

d/dx (u^n) = nu^(n-1) du/dx

d/dx (sin^-1 x) =

1/√(1-x^2) d/dx

d/dx (cos^-1 x) =

-d/dx sin^-1 x

d/dx (tan^-1 x) =

1/(1+x^2) d/dx

d/dx (csc^-1 x) =

-d/dx sec^-1 x

d/dx (sec^-1 x) =

1/|x|√x^2-1 d/dx

d/dx (cot^-1 x) =

-d/dx tan^-1 x

lim x->0 (sin ax)/ax =

1

lim x->∞ (sin x)/x =

0

lim x->0 1/(sin x) =

DNE

lim x->0 (cos x - 1)/x =

0

lim x->∞ (1 + 1/n)^n =

e