Question

Find the derivative of the given function: square root of (ex) ......I thought the answer was 1/2ex^-1/2


* They say the answer is 1/2 sqrt (e/x)

Answer 1

\[\sqrt{ex}=\sqrt{e}\sqrt{x}\]
so
\[\sqrt{e}(x^\frac{1}{2})'=\sqrt{e} \cdot \frac{1}{2} x^{\frac{1}{2}-1}=\sqrt{e} \cdot \frac{1}{2} x^\frac{-1}{2}\]
\[=\sqrt{e} \cdot \frac{1}{2} \cdot \frac{1}{\sqrt{x}}\]

Answer 2

\[=\frac{1}{2} \cdot \sqrt{\frac{e}{x}}\]