What is the first derivative of xf(x) ?

The first derivative of xf(x) is 2xf

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derivative of xf(x)

derivative of

x f (x)

2 x f

Solution steps

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

Simplify

x f x : x^{2} f

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

Treat

f

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 x f