What is the derivative of sqrt(xe^x) ?

The derivative of sqrt(xe^x) is (e^x+e^xx)/(2sqrt(e^xx))

What is the first derivative of sqrt(xe^x) ?

The first derivative of sqrt(xe^x) is (e^x+e^xx)/(2sqrt(e^xx))

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

\frac{e ^{x} + e ^{x} x}{2 e ^{x} x}

Solution steps

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

Apply the chain rule:

\frac{1}{2 x e ^{x}} \frac{d}{d x} (x e^{x})

= \frac{1}{2 x e ^{x}} \frac{d}{d x} (x e^{x})

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

= \frac{1}{2 x e ^{x}} (e^{x} + e^{x} x)

Simplify

\frac{1}{2 x e ^{x}} (e^{x} + e^{x} x) : \frac{e ^{x} + e ^{x} x}{2 e ^{x} x}

= \frac{e ^{x} + e ^{x} x}{2 e ^{x} x}

What is the derivative of sqrt(xe^x) ?
The derivative of sqrt(xe^x) is (e^x+e^xx)/(2sqrt(e^xx))
What is the first derivative of sqrt(xe^x) ?
The first derivative of sqrt(xe^x) is (e^x+e^xx)/(2sqrt(e^xx))