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

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Answer 1 · 2018-01-25T17:20:29

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

Use the chain rule for this derivative:

#d/dx((ln(x))^3) = 3(ln(x))^2*d/dx(ln(x))=(3(ln(x))^2)/x#.

Alternatively #y=u^3# and #u=ln(x)#:

#dy/(dx)=dy/(du)*(du)/(dx)#

#dy/(dx)=3u^2*1/x# and substituting #dy/(dx)=(3(ln(x))^2)/x#