Question

How do you find the derivative of `y=ln ln(2x^4)`?

Answer 1

`(dy)/(dx) = 4/(xln(2x^4))`

Explanation:

Using the chain rule we know that in general:

`d/(dx) ln f(x) = (f'(x))/f(x)`

Apply this formula iteratively:

`(dy)/(dx) = (d(lnln(2x^4)))/(dx) = 1/ln(2x^4) (d(ln(2x^4)))/(dx) =`

`= 1/ln(2x^4)1/(2x^4)(d(2x^4))/(dx) = 1/ln(2x^4)*1/(2x^4)*8x^3 = 4/(xln(2x^4))`