Mathematics Cheat Sheet

Exponents

Product

ax × ay = ax + y

Quotient

ax ÷ ay = ax - y

Power

axy = ax × y

Logarithms

Product

log(a×b) = log(a) + log(b)

Quotient

log(a÷b) = log(a) - log(b)

Power

log(axy) = y × log(ax)

Derivatives

Power

xa → a×xa−1

Logarithm

logax → 1/(x×ln(a))

Constant to a Power

ax → ln(a)ax

Product

uv → uv' + vu'

Quotient

uv → (vu' − uv') / v2

Chain Rule

f(g(x)) → f`(g(x))g`(x)

Sin

sin(x) → cos(x)dx

Cos

cos(x) → −sin(x)dx

Tangent

tan(x) → sec2(x)dx

Volume

Volume

2 pi integral a b xf(x)dx