What is the derivative of (ln (x-4)) ^ 3(ln(x4))3?

1 Answer
Jul 3, 2016

The reqd. deri. ={3(ln(x-4))^2)/(x-4)=3(ln(x4))2x4.

Explanation:

Let y=(ln(x-4))^3y=(ln(x4))3, & put t=ln(x-4)t=ln(x4), so, y=t^3............(1)

So, y is a fun. of t & t of x.

By Chain Rule, then, we have, the reqd. deri. =dy/dx=dy/dt*dt/dx
=d/dt(t^3)*d/dx{ln(x-4)}..........[by (1)]

=3t^2*{1/(x-4)}*d/dx(x-4)=(3t^2)/(x-4)*1={3(ln(x-4))^2)/(x-4).