Oh no! Fractional derivatives!

We know that $g(x) = \cfrac{d^{0.5}}{dx^{0.5}}\big( f(x) \big)$

If we take the $1.5^{\text{th}}$ derivative of $g(x)$ , we get $\begin{aligned} \frac{d^{1.5}}{dx^{1.5}} \left( \frac{d^{0.5}}{dx^{0.5}}\big( f(x) \big)\right) &= \frac{d^{1.5 + 0.5}}{dx^{1.5 + 0.5}}\big( f(x) \big) \\ &= \frac{d^{2}}{dx^{2}}\left( x^{\frac{3}{5}} \right) \\ &= -\frac{6}{25x^{\frac{7}{5}}} \end{aligned}$

Now we can plug in $32$ and the answer is $-\frac{6}{25(32)^{\frac{7}{5}}} = \green{\boxed{-0.001875}}$