Question

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

Answer 1

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

Explanation:

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