What is the first derivative of xinx ?

The first derivative of xinx is 2inx

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derivative of xinx

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

2 in x

Solution steps

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

Simplify

x in x : in x^{2}

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 in x