Formulas and rules
Every key math formula and rule, organised by topic and school level, with examples and study tips.
Calculus 4
Derivative of a power
d/dx (x^n) = n x^(n-1)
Bring the power down and reduce it by one.
Sum, product and quotient rules
(uv)' = u'v + uv' ; (u/v)' = (u'v - uv') / v^2
Differentiate sums term by term; use the product and quotient rules for combinations.
Tangent line and stationary points
y = f(a) + f'(a)(x - a)
The derivative at a point is the slope of the tangent. Stationary points have f'(x) = 0.
Integrals
integral of x^n = x^(n+1)/(n+1) + C
Integration undoes differentiation and measures the area under a curve.