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

The answer to (\partial)/(\partial x)(sqrt(x)y) is y/(2sqrt(x))

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

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

\frac{y}{2 x}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{y}{2 x}

\frac{d}{d x} (ln (0))

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

\frac{d}{d x} (x ln (2 x + 1))

\frac{d}{d x} (\frac{1}{3} cos (3 x))

\frac{d}{d x} ((2 x - 4)^{4} (x^{2} + x + 1)^{5})

What is (\partial)/(\partial x)(sqrt(x)y) ?
The answer to (\partial)/(\partial x)(sqrt(x)y) is y/(2sqrt(x))