What is the derivative of ${sin (x)}^{\frac{1}{2}}$ $sin(x)^(1/2)$ ?

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Answer 1 · 2016-08-11T17:59:08

$\frac{d}{d x} f (x) = \frac{cos (x)}{2 \cdot \sqrt{sin (x)}}$ $d/(d x) f(x)=(cos(x))/(2*sqrt sin(x))$

$f (x) = {sin (x)}^{\frac{1}{2}}$ $f(x)=sin(x)^(1/2)$

$\frac{d}{d x} f (x) = \frac{1}{2} \cdot {sin (x)}^{(\frac{1}{2} - 1)} \cdot cos (x)$ $d/(d x) f(x)= 1/2*sin(x)^((1/2-1))*cos (x)$

$\frac{d}{d x} f (x) = \frac{1}{2} \cdot {sin (x)}^{- \frac{1}{2}} \cdot cos (x)$ $d/(d x) f(x)=1/2*sin(x)^(-1/2)*cos (x)$

$\frac{d}{d x} f (x) = \frac{cos (x)}{2 \cdot \sqrt{sin (x)}}$ $d/(d x) f(x)=(cos(x))/(2*sqrt sin(x))$

What is the derivative of sin(x)12sin(x)^(1/2) ?