$$(\frac{3}{10})^{5}\times(\frac{2}{15})^{5}\cdot C$$
$\frac{C}{9765625}$
$$\frac{243}{100000}\times \left(\frac{2}{15}\right)^{5}C$$
$$\frac{243}{100000}\times \frac{32}{759375}C$$
$$\frac{243\times 32}{100000\times 759375}C$$
$$\frac{7776}{75937500000}C$$
$$\frac{1}{9765625}C$$
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$\frac{1}{9765625} = 1.024 \times 10^{-7}$
$$\frac{\mathrm{d}}{\mathrm{d}C}(\frac{243}{100000}\times \left(\frac{2}{15}\right)^{5}C)$$
$$\frac{\mathrm{d}}{\mathrm{d}C}(\frac{243}{100000}\times \frac{32}{759375}C)$$
$$\frac{\mathrm{d}}{\mathrm{d}C}(\frac{243\times 32}{100000\times 759375}C)$$
$$\frac{\mathrm{d}}{\mathrm{d}C}(\frac{7776}{75937500000}C)$$
$$\frac{\mathrm{d}}{\mathrm{d}C}(\frac{1}{9765625}C)$$
$$\frac{1}{9765625}C^{1-1}$$
$$\frac{1}{9765625}C^{0}$$
$$\frac{1}{9765625}\times 1$$
$$\frac{1}{9765625}$$
