Higher-order Derivatives

 Definitions and properties

Second derivative

f′′=ddx(dydx)−d2ydx2

Higher-Order derivative

f(n)=(f(n−1))′

(f±g)(n)=f(n)± g(n)

Leibniz's Formulas

(f⋅g)′′=f′′⋅g+2⋅f′⋅g′+f⋅g′′

(f⋅g)′′′=f′′′⋅g+3⋅f′′⋅g′+3⋅f′⋅g′′+f⋅g′′′

(f⋅g)(n)=f(n)⋅g+n⋅f(n−1)⋅g′+n(n−1)1⋅2⋅f(n−2)⋅g′′+⋯+f⋅g(n)