How do you find the first and second derivative of ${ln x}^{\frac{1}{2}}$ $lnx^(1/2)$ ?

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Answer 1 · 2016-06-14T07:03:37

$f'(x)=1/(2x)$ and $f''(x)=-1/(2x^2)$

We use the concept of function of a function according to which,.

$d/(dx)f(g(x))=(df)/(dg)xx(dg)/(dx)$

Hence as $f(x)=lnx^(1/2)$

$f'(x)=1/x^(1/2)xx1/2x^(-1/2)=1/(2x)$

and $f''(x)=1/2xx(-1)/x^2=-1/(2x^2)$

How do you find the first and second derivative of lnx^(1/2)lnx12lnx^(1/2)?