What is the first derivative of-x^3 ?

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

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derivative of-x^3

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

- 3 x^{2}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

= - 3 x^{3 - 1}

Simplify

= - 3 x^{2}