<s>[INST] How do I differentiate to what they have given? Given that  $y = \dfrac{x^3 - 5x}{\sqrt{x}}$, show that $\dfrac{dy}{dx}$= $\dfrac{5(x^2 - 1)}{2 \sqrt{x}}$ 
(Posted from ``answer'' below: I get as far as  $\dfrac{dy}{dx}= \dfrac {5}{2}x^\frac {3}{2}  - \dfrac {5}{2}x^\frac{-1}{2}$  but struggling with the first fraction.)
I am just getting to grips with the formatting so hope that is clear! 
Many thanks
 [/INST] $\dfrac{dy}{dx}=\dfrac{(3x^2-5)\sqrt{x}-\frac{x^3-5x}{2\sqrt{x}}}{x}=\frac{3x^2-5}{\sqrt{x}}-\frac{x^2-5}{2\sqrt{x}}=\frac{5(x^2-1)}{2\sqrt{x}}$
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