<s>[INST] Find the derivative of the function $f(x)=(5-x^2)(\sqrt{x})$ I am stuck on this question, not sure what I am doing wrong:
\begin{align*}
 f(x) &=(5-x^2)(\sqrt{x}) \\
\\
 f'(x) &=(5-x^2)(x)^{1/2} \\
&=(-2x)(x)^{1/2}+(-x^2+5)(\dfrac{1}{2})(x)^{-1/2}\\
&=-2x^{3/2}+\dfrac{1}{2}(-x^{3/2}+5x^{-1/2})\\
&=\dfrac{1}{2}x^{-1/2}\bigg(x^2-2x^2+10\bigg)\\
&=\dfrac{1}{2}x^{-1/2}\bigg(-x^2+10\bigg)
\end{align*}
 [/INST] Answer
In your fourth step:
$f'(x) = \frac{-5}{2}x^{\frac{3}{2}} + \frac{5}{2}x^{\frac{-1}{2}}$
$f'(x) =-\frac{5}{2}\left(\frac{x^2 -1}{\sqrt{x}}\right)$
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