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Popular >

derivative of sqrt(xe^x)

Solution

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

Solution

\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}

Popular Examples

derivative of cos(4x-sin(x))

\frac{d}{d x} (cos (4 x) - sin (x))

integral of (-7x^2)/(sqrt(4x-x^2))

\int \frac{- 7 x ^{2}}{4 x - x ^{2}} d x

sum from n=1 to infinity of 2/(3n+1)

n = 1 \sum \infty \frac{2}{3 n + 1}

integral of 2xln(4x)

\int 2 x ln (4 x) d x

slope of (6.9)(7.1)slope

(6.9) (7.1)

Frequently Asked Questions (FAQ)

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))