State and prove leibnitzs theorem to find the nth derivative of a product of two function of x - Maths - Application of Derivatives

Question

State and prove leibnitzs theorem to find the nth derivative of a
product of two function of x

Ghanshyam Dhakar · Accepted Answer

Dear student,
leibnitz theorem  let y=ux vxddxu
v=uv1+u1vd2dx2u
v=uv2+u1v1+u1v1+u2v                  =uv2+2u1v1+u2v                  =C02uv2+C12u1v1+C22u2vd3dx3u
v=uv3+u1v2+2u1v2+2u2v1+u3v+u2v1                    =uv3+3u1v2+3u2v1+u3v                     =C03uv3+C13u1v2+C23u2v1+C33u3vthen nth derivative dndxnu
v  =C0nuvn+C1nu1vn-1+C2nu2vn-2+C3nu3vn-3+  
  +Cnnunv
Regards