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Take y=x²e
take ln on both sides
ln y=2lnx+1
diff. w.r.t x on both sides
 \frac{1}{y} \frac{dy}{dx}= \frac{2}{x}
 \frac{dy}{dx}= \frac{2y}{x}= \frac{2x^2e}{x}=2xe

short method:
 \frac{dy}{dx}= \frac{d}{dx}( x^{2} e)=2xe

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