What is the derivative of-8x^3 ?

The derivative of-8x^3 is -24x^2

What is the first derivative of-8x^3 ?

The first derivative of-8x^3 is -24x^2

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\frac{d}{d x} (- 8 x^{3})

- 24 x^{2}

Solution steps

\frac{d}{d x} (- 8 x^{3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 8 \frac{d}{d x} (x^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - 8 \cdot 3 x^{3 - 1}

Simplify

= - 24 x^{2}