Rules of differentiation

Answer 1

Assume f=f(x), g=g(x)and (f^-1)(x) is the functional inverse of f(x).

(f+g)'=f'+g'

(f*g)'=f'*g+f*g' product rule

(f(g))'=g'*f'(g) compositional rule

(f/g)'=(f'*g-f*g')/(g^2) quotient rule

(d/dx)(x^r)=r*x^(r-1) power rule and applies for ALL r.

where g^2 is g*g not g(g)