$$\frac{b^{6}}{15}\cdot\frac{5}{b^{3}}=$$
$\frac{b^{3}}{3}$
$$\frac{b^{6}\times 5}{15b^{3}}$$
$$\frac{b^{3}}{3}$$
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$b^{2}$
$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b^{6}\times 5}{15b^{3}})$$
$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b^{3}}{3})$$
$$3\times \frac{1}{3}b^{3-1}$$
$$b^{3-1}$$
$$b^{2}$$
