Calculus

Simple Compound interest formula

A(t) = P(1+r/n) ^nt

radians to degrees

x 180/π

degrees to radians

x π/180

Tangent Line Definition

instantaneous slope of a line at ONE point

secant line definition

the slope between 2 points

pythagorean identity

cos^2x + sin^2x = 1

calculating the slope of a secant line

f(b) - f(a)/b-a OR limit definition

Limit definition

f(x+h)-f(x)/h

1/sin(x)

csc(x)

1/cos(x)

sec(x)

1/tan(x)

cot(x)

d/dx (√x)

1/2√x

power rule

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

chain rule

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

general power rule

d/dx [g(x)]^r = r [g(x)]^r-1 times g'(x)

d/dx sec(x)

sec(x)tan(x)

product rule

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

quotient rule

u/v = (u'v - v'u) / v²

lim (x->0) sinx/x

1

lim (x->0) (1-cosx)/x

0

d/dx cos(x)

- sin(x)

d/dx sin(x)

cos(x)

d/dx e^x

e^x

d/dx (e)^f(x)

f'(x)e^f(x)

lne

1

d/dx lnx

1/x

d/dx ln f(x)

f'(x)/f(x)

d/dx lny

y'/y

are endpoints differentiable?

NO

e^0

1

d/dx (e^-x)

-e^-x

what should you do when finding extrema on a closed interval?

check endpoints!

d/dx (sin^-1x)

1/√(1-x²)

d/dx (cos^-1x)

-1/√(1-x²)

d/dx (tan^-1x)

1/(1+x²)

Area of a circle

πr²

Circumference of a circle

2πr

Volume of a sphere

4/3πr³

Surface area of a sphere

4πr²

volume of a cylinder

V=πr²h

Surface area of a cylinder

2πr² + 2πrh

d/dx tan(x)

sec²x

antiderivative of sec²x

tan(x) + c

antiderivative of lnx/x

lnx²/2

ln(1)

= 0

antiderivative of du / (u²+1)

tan^-1 (u)