How do you differentiate $x {(ln x)}^{2}$ $x(lnx)^2$ ?

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Answer 1 · 2016-06-09T15:07:19

Use the product rule and simplify.
$\frac{d}{d x} [x \cdot {ln}^{2} (x)] = ln (x) [ln (x) + 2]$ $d/dx [ x * ln^2(x) ] = ln(x) [ ln(x) +2 ]$

$\frac{d}{d x} [x \cdot {ln}^{2} (x)]$ $d/dx [ x * ln^2(x) ]$

$= (\frac{d}{d x} [x] \cdot {ln}^{2} (x)) + (x \cdot \frac{d}{d x} [{ln}^{2} (x)])$ $= (d/dx [ x ]* ln^2(x)) +( x * d/dx [ ln^2(x) ] )$

$= (1 \cdot {ln}^{2} (x)) + (x \cdot \frac{d}{d x} [ln (x)] \cdot 2 ln (x))$ $= (1* ln^2(x)) +( x * d/dx [ ln(x) ] * 2 ln(x))$

$= ({ln}^{2} (x)) + (x \cdot \frac{1}{x} \cdot 2 ln (x))$ $= ( ln^2(x)) +( x * 1/x * 2 ln(x))$

$= ({ln}^{2} (x)) + (2 ln (x))$ $= ( ln^2(x)) +(2 ln(x))$

$= ln (x) [ln (x) + 2]$ $= ln(x) [ ln(x) +2 ]$

How do you differentiate x(lnx)2x(lnx)^2?