$$(-7-7v- { v }^{ 3 } )+(-5 { v }^{ 4 } + { v }^{ 3 } +8v$$
$-5v^{4}+v-7$
$$-7-7v-5v^{4}+8v$$
$$-7+v-5v^{4}$$
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$1-20v^{3}$
$$\frac{\mathrm{d}}{\mathrm{d}v}(-7-7v-5v^{4}+8v)$$
$$\frac{\mathrm{d}}{\mathrm{d}v}(-7+v-5v^{4})$$
$$v^{1-1}+4\left(-5\right)v^{4-1}$$
$$v^{0}+4\left(-5\right)v^{4-1}$$
$$v^{0}-20v^{4-1}$$
$$v^{0}-20v^{3}$$
$$1-20v^{3}$$
