Question

(If
y = log (axtb)
Find
Yn​

Answer 1

solution:

=log(ax+x^2)

dy/dx = 1/(ax + b ) x a = a/ (ax +b)

d^2y/dx^2 = -1/(ax + b) x a x a = - a^2/(ax +b)^2

d^3 / dx^3  = 2a^3/(ax + b )^3 = (-1) ^3+1 x 2a^3/(ax +b)^3

in general

d^ny/dx^n = (-1)^n+1 x (n-1)a^n/(ax + b)^n