What is (\partial)/(\partial x)(sqrt(xye^y)) ?

The answer to (\partial)/(\partial x)(sqrt(xye^y)) is (e^ysqrt(y))/(2sqrt(x)\sqrt{e^y)}

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(\partial)/(\partial x)(sqrt(xye^y))

\frac{\partial}{\partial x} (x y e^{y})

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

Solution steps

\frac{\partial}{\partial x} (x y e^{y})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x y e ^{y}} \frac{\partial}{\partial x} (x y e^{y})

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

\frac{\partial}{\partial x} (x y e^{y}) = y e^{y}

= \frac{1}{2 x y e ^{y}} y e^{y}

Simplify

\frac{1}{2 x y e ^{y}} y e^{y} : \frac{e ^{y} y}{2 x e ^{y}}

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

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\int_{0}^{2 π} sin^{2} (x) d x

n = 1 \sum \infty n^{- \frac{1}{5}}

x \to 2 - lim (\frac{5 x}{x - 6})

f (x) = (x^{3} + 2) e^{x}

What is (\partial)/(\partial x)(sqrt(xye^y)) ?
The answer to (\partial)/(\partial x)(sqrt(xye^y)) is (e^ysqrt(y))/(2sqrt(x)\sqrt{e^y)}