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)