$$3x \div { x }^{ -2 } + { x }^{ 2 } \times { x }^{ 1 } - \frac{ 16 { x }^{ 1 } }{ 2 { x }^{ -2 } }$$
$-4x^{3}$
$$\frac{3x}{x^{-2}}+x^{3}-\frac{16x^{1}}{2x^{-2}}$$
$$3x^{3}+x^{3}-\frac{16x^{1}}{2x^{-2}}$$
$$4x^{3}-\frac{16x^{1}}{2x^{-2}}$$
$$4x^{3}-\frac{8x^{1}}{x^{-2}}$$
$$4x^{3}-8x^{3}$$
$$-4x^{3}$$
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$-12x^{2}$
$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x}{x^{-2}}+x^{3}-\frac{16x^{1}}{2x^{-2}})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}+x^{3}-\frac{16x^{1}}{2x^{-2}})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}-\frac{16x^{1}}{2x^{-2}})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}-\frac{8x^{1}}{x^{-2}})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}-8x^{3})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{3})$$
$$3\left(-4\right)x^{3-1}$$
$$-12x^{3-1}$$
$$-12x^{2}$$
