$$\frac { 5 x ^ { 2 } y ^ { 9 } } { 15 y ^ { 9 } x ^ { 4 } }$$
$\frac{1}{3x^{2}}$
$$\frac{5^{1}x^{2}y^{9}}{15^{1}x^{4}y^{9}}$$
$$\frac{5^{1}}{15^{1}}x^{2-4}y^{9-9}$$
$$\frac{5^{1}}{15^{1}}x^{-2}y^{9-9}$$
$$\frac{5^{1}}{15^{1}}\times \frac{1}{x^{2}}y^{0}$$
$$\frac{5^{1}}{15^{1}}\times \frac{1}{x^{2}}$$
$$\frac{1}{3}\times \frac{1}{x^{2}}$$
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$-\frac{2}{3x^{3}}$
$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{9}}{15y^{9}}x^{2-4})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3}x^{-2})$$
$$-2\times \frac{1}{3}x^{-2-1}$$
$$-\frac{2}{3}x^{-3}$$
