Solve for: /(d) d s [ 2 s ^ 3-4 s ^-2+8 s ^-8 ] =

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Expression: $$\frac { d } { d s } [ 2 s ^ { 3 } - 4 s ^ { - 2 } + 8 s ^ { - 8 } ] =$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is $0$. The derivative of $ax^{n}$ is $nax^{n-1}$.

$$3\times 2s^{3-1}-2\left(-4\right)s^{-2-1}-8\times 8s^{-8-1}$$

Multiply $3$ times $2$.

$$6s^{3-1}-2\left(-4\right)s^{-2-1}-8\times 8s^{-8-1}$$

Subtract $1$ from $3$.

$$6s^{2}-2\left(-4\right)s^{-2-1}-8\times 8s^{-8-1}$$

Multiply $-2$ times $-4$.

$$6s^{2}+8s^{-2-1}-8\times 8s^{-8-1}$$

Subtract $1$ from $-2$.

$$6s^{2}+8s^{-3}-8\times 8s^{-8-1}$$

Multiply $-2$ times $-4$.

$$6s^{2}+8s^{-3}-64s^{-8-1}$$

Subtract $1$ from $-8$.

$$6s^{2}+8s^{-3}-64s^{-9}$$

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