How do you find the derivatives of y=(lnx)^3?

1 Answer
Feb 18, 2017

dy/dx = 3((ln(x))^2/x)

Explanation:

We can apply Chain Rule of Differentiation.

d/dx f@g(x)= [d/dx f(u)][d/dx u]

or

[f@g(x)]' = {f'[g(x)]}{g'(x)}

Let u = lnx and f(x) = (...)^3

d/dx f@g(x) =[3(lnx)^2][d/dx lnx]

d/dx f@g(x) =[3(lnx)^2][1/x]

d/dx f@g(x) = 3((lnx)^2/x)