What is the derivative of ${(ln x)}^{2}$ $(lnx)^2$ ?

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Answer 1 · 2015-12-29T19:59:26

Chain rule states that $\frac{d y}{d x} = \frac{d y}{d u} \frac{d u}{d x}$ $(dy)/(dx)=(dy)/(du)(du)/(dx)$

Renaming $u = ln x$ $u=lnx$ , we get that:

$\frac{d y}{d x} = 2 u \frac{1}{x} = \frac{2 u}{x} = \frac{2 (ln x)}{x}$ $(dy)/(dx)=2u1/x=(2u)/x=(2(lnx))/x$

What is the derivative of (lnx)2(lnx)^2?