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

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

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(\partial)/(\partial y)(xy^{1/2})

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\frac{d}{d x} ((3 - x^{2}) (x^{3} - 5 x + 2))

\frac{d x}{d t} = t x - 2 x + t - 2

\int \frac{x}{4 + 9 x ^{2}} d x

x \to 0 lim (\frac{1 - cot ( x )}{\frac{1}{x}})

5 + x^{2}

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