What is (\partial)/(\partial x)(8x^{0.5}y^{0.5}) ?

The answer to (\partial)/(\partial x)(8x^{0.5}y^{0.5}) is (4y^{1/2})/(x^{0.5)}

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(\partial)/(\partial x)(8x^{0.5}y^{0.5})

\frac{\partial}{\partial x} (8 x^{0.5} y^{0.5})

\frac{4 y ^{\frac{1}{2}}}{x ^{0.5}}

Solution steps

\frac{\partial}{\partial x} (8 x^{0.5} y^{0.5})

Treat

y

as a constant

Take the constant out:

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

= 8 y^{0.5} \frac{\partial}{\partial x} (x^{0.5})

Apply the Power Rule:

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

= 8 y^{0.5} \cdot 0.5 x^{0.5 - 1}

Simplify

8 y^{\frac{1}{2}} \cdot 0.5 x^{0.5 - 1} : \frac{4 y ^{\frac{1}{2}}}{x ^{0.5}}

= \frac{4 y ^{\frac{1}{2}}}{x ^{0.5}}

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What is (\partial)/(\partial x)(8x^{0.5}y^{0.5}) ?
The answer to (\partial)/(\partial x)(8x^{0.5}y^{0.5}) is (4y^{1/2})/(x^{0.5)}