What is the first derivative of 2x^4 ?

The first derivative of 2x^4 is 8x^3

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derivative of 2x^4

derivative of

2 x^{4}

8 x^{3}

Solution steps

\frac{d}{d x} (2 x^{4})

Take the constant out:

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

= 2 \frac{d}{d x} (x^{4})

Apply the Power Rule:

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

= 2 \cdot 4 x^{4 - 1}

Simplify

= 8 x^{3}