What is the first derivative of xex ?

The first derivative of xex is 2ex

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derivative of xex

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

2 e x

Solution steps

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

Simplify

x e x : e x^{2}

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

Take the constant out:

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

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

Apply the Power Rule:

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

= e 2 x^{2 - 1}

Simplify

= 2 e x

y^{^{''}} - 2 y^{^{'}} + 5 y = 17 cos (2 x)

\int x (12 x + 8) d x

x \to 0 lim (e^{- \frac{1}{x}})

\frac{d y}{d x} = \frac{2 x y}{x ^{2} + y ^{2}}

\int (- 9 x^{2} + 9 x + 2) d x