What is the first derivative of xn(x) ?

The first derivative of xn(x) is 2nx

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derivative of xn(x)

\frac{d}{d x} (x n (x))

2 n x

Solution steps

\frac{d}{d x} (x n (x))

Simplify

x n (x) : n x^{2}

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 n x