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

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

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Answer 1 · 2017-10-22T04:53:30

see below.

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

$\frac{d y}{d x} = x^{2} \frac{d}{d x} ln (2 x) + ln (2 x) \frac{d}{d x} x^{2}$ $dy/dx=x^2d/dxln(2x)+ln(2x)d/dxx^2$

$= x^{2} (\frac{1}{2} x) \frac{d}{d x} 2 x + ln (2 x) (2 x)$ $=x^2(1/2x)d/dx2x+ln(2x)(2x)$

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

$= x + 2 x ln (2 x)$ $=x+2xln(2x)$