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Popular >

derivative of sqrt(w)e^w

Solution

derivative of

w e^{w}

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = w, g = e^{w}

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

\frac{d}{d w} (w) = \frac{1}{2 w}

\frac{d}{d w} (e^{w}) = e^{w}

= \frac{1}{2 w} e^{w} + e^{w} w

\frac{1}{2 w} e^{w} = \frac{e ^{w}}{2 w}

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

Graph

Popular Examples

(\partial)/(\partial x)((x^{5/7})/(e^x))

\frac{\partial}{\partial x} (\frac{x ^{\frac{5}{7}}}{e ^{x}})

limit as x approaches 0 of 2/(x^2+x)-2/x

x \to 0 lim (\frac{2}{x ^{2} + x} - \frac{2}{x})

derivative of (3t^2+4t-8)/(t^{3/2)}derivative of

\frac{3 t ^{2} + 4 t - 8}{t ^{\frac{3}{2}}}

limit as x approaches 0 of x^3-4x^2+9x-2

x \to 0 lim (x^{3} - 4 x^{2} + 9 x - 2)

integral of cos(2x)2x

\int cos (2 x) d^{2} x d x

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(w)e^w ?
The derivative of sqrt(w)e^w is (e^w)/(2sqrt(w))+e^wsqrt(w)
What is the first derivative of sqrt(w)e^w ?
The first derivative of sqrt(w)e^w is (e^w)/(2sqrt(w))+e^wsqrt(w)