$$(12 { x }^{ 3 } y4) \div (-2x { y }^{ 2 } )$$
$-6\times \left(\frac{x}{y}\right)^{2}y_{4}$
$$\frac{6y_{4}x^{2}}{-y^{2}}$$
$$\frac{-6y_{4}x^{2}}{y^{2}}$$
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$-\frac{12xy_{4}}{y^{2}}$
$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12y_{4}}{-2y^{2}}x^{3-1})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{6y_{4}}{y^{2}}\right)x^{2})$$
$$2\left(-\frac{6y_{4}}{y^{2}}\right)x^{2-1}$$
$$\left(-\frac{12y_{4}}{y^{2}}\right)x^{1}$$
$$\left(-\frac{12y_{4}}{y^{2}}\right)x$$
