What is the first derivative of xdx ?

The first derivative of xdx is 2xd

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derivative of xdx

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

2 x d

Solution steps

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

Simplify

x d x : x^{2} d

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

Treat

d

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 x d

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