What is the first derivative of u^3 ?

The first derivative of u^3 is 3u^2

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derivative of u^3

derivative of

u^{3}

3 u^{2}

Solution steps

\frac{d}{d u} (u^{3})

Apply the Power Rule:

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

= 3 u^{3 - 1}

Simplify

= 3 u^{2}

\frac{d}{d x} (12 + 4 x - x^{2})

\frac{d}{d x} (1 + 2 x - x^{3})

\int (\frac{1}{( 1 + x ) ^{2}}) d x

\int_{1}^{\infty} x e^{- 3 x} d x

\frac{d}{d x} (2 x e^{2 x} + e^{2 x} \cdot 2 x^{2})