Answer
$f''(x) = (\frac{225}{4})\sqrt x$
Work Step by Step
1. Find $f'(x)$
$f(x) = 15x^{\frac{5}{2}}$
$f'(x) = (15 \times \frac{5}{2})x^{(\frac{5}{2} - 1)}$
$f'(x) = (\frac{75}{2})x^{(\frac{3}{2})}$
2. Find $f''(x)$
$f'(x) = (\frac{75}{2})x^{(\frac{3}{2})}$
$f''(x) = (\frac{75}{2} \times \frac{3}{2})x^{(\frac{3}{2}- 1)}$
$f''(x) = (\frac{225}{4})x^{\frac{1}{2}}$
$f''(x) = (\frac{225}{4})\sqrt x$
