Calculus basics (Class 11–12)

Power rule

d/dx xⁿ = nxⁿ⁻¹

Product rule

(uv)′ = u′v + uv′

Quotient rule

(u/v)′ = (u′v − uv′)/v²

Chain rule

dy/dx = (dy/du)(du/dx)

Derivatives of sin, cos

(sin x)′ = cos x; (cos x)′ = −sin x

Derivatives of eˣ, ln x

(eˣ)′ = eˣ; (ln x)′ = 1/x

Power integral

∫xⁿ dx = xⁿ⁺¹/(n + 1) + C, n ≠ −1

Integral of 1/x

∫(1/x) dx = ln|x| + C

Integration by parts

∫u dv = uv − ∫v du

Definite integral

∫ₐᵇ f(x) dx = F(b) − F(a)

F′ = f