What is (\partial)/(\partial x)(x^{1/2}*y) ?

The answer to (\partial)/(\partial x)(x^{1/2}*y) is y/(2x^{1/2)}

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(\partial)/(\partial x)(x^{1/2}*y)

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 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{1}{2}}}

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

What is (\partial)/(\partial x)(x^{1/2}*y) ?
The answer to (\partial)/(\partial x)(x^{1/2}*y) is y/(2x^{1/2)}