Important equations to memorise

Difference of two squares

a² - b² = (a+b)(a-b)

Logs1

lnab = lna + lnb

Logs2

lna/b = lna - lnb

Chain rule (when a function is within a function)

du/dx * dy/du

Product rule (when multiplying two functions together)

u*dv/dx + v*du/dx

Parametric differentiation

(dy/dt)/(dx/dt) → y is still on top and x is still on bottom like dy/dx

Arithmetic term

u_n = a + (n-1)d

where a is the first term in the series

where d is the common Difference

Sum of the terms up to n

S_n = n/2(a+l)

S_n = n/2(2a + (n-1)d) ——> same equation with u_n subbed in

Geometric term

u_n = ar^n-1 where r is the common Ratio