Chapter 3 Calculus Rules

derivative of a constant

0

by power rule x^n becomes

nx^(n-1)

constant multiple rule: d/dx(c*f(x))

c*d/dxf(x)

sum/difference rule: d/dx f(x)+-g(x)

d/dx f(x) +- d/dx g(x)

derivative of e^x

e^x

product rule

1st D 2nd + 2nd D 1st

quotient rule:

Low D-high minus high D-low, all over low-low

derivative of sin x

cos x

derivative of cos x

-sinx

derivative of tan x

sec²x

derivative of sec x

secxtanx

derivative of csc x

-cscxcotx

derivative of cot x

-csc²x

chain rule

derivative of outer function; put inner function inside; multiply by derivative of inner function

derivative of a^x

a^xlna

lim x→0 (cos x - 1)/x

0

lim x→0 sin x/x

1

lim x→0 (sin ax)/ax

1

sin(a±b)

sinacosb±cosasinb

cos (a±b)

cosacosb∓sinasinb