unit 2 derivative proofs

power rule

nx^n-1

derivative of a constant function

d/dx ( c ) = 0

sum and difference rule

u^I(x)+v^I(x)

constant multiple rule

c • u^I(x)

derivative of the sine function

cos(x)

derivative of the cosine function

-sin(x)

important exponetial limit #1

e^h-1/h = 1

important exponetial limit #2

a^h-1/h = ln(a)

e^x

e^x

a^x (if a > 0 and a is not equal to 1)

a^x…ln(a)

ln(x)

1/x

log_ax

1/xlna

the product rule [ u(x) • v(x) ]

v^I(x)u(x)+u^I(x)v(x)

the quotient rule [ u(x) / v(x) ]

u^I(x)v(x)-v^I(x)u(x) / [v(x)]²

tanx

sec²x

sec(x)

tan(x) • sec (x)

cot(x)

-csc²(x)

csc(x)

-csc(x)cot(x)