How do you differentiate $f (x) = (x^{\frac{1}{2}}) (ln x)$ $f(x)=(x^(1/2))(lnx)$ ?

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Answer 1 · 2017-02-25T23:17:48

$\frac{1}{2 \sqrt{x}} ln x + \frac{1}{\sqrt{x}}$ $1/(2sqrtx) lnx+ 1/sqrtx$

This needs to be differentiated using the product rule:

$d/dxf(x)g(x)=g(x)f'(x)+f(x)g'(x)$

$d/dx x^(1/2)= 1/2x^(-1/2)= 1/(2sqrtx)$

$d/dxlnx= 1/x$

$d/dxf(x)=1/(2sqrtx)lnx+sqrtx/x=1/(2sqrtx)+1/sqrtx$

How do you differentiate f(x)=(x^(1/2))(lnx)f(x)=(x12)(lnx)f(x)=(x^(1/2))(lnx)?