What is (\partial)/(\partial x)(x^{0.25}y^{0.5}) ?

The answer to (\partial)/(\partial x)(x^{0.25}y^{0.5}) is (0.25y^{1/2})/(x^{0.75)}

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(\partial)/(\partial x)(x^{0.25}y^{0.5})

\frac{\partial}{\partial x} (x^{0.25} y^{0.5})

\frac{0.25 y ^{\frac{1}{2}}}{x ^{0.75}}

Solution steps

\frac{\partial}{\partial x} (x^{0.25} y^{0.5})

Treat

y

as a constant

Take the constant out:

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

= y^{0.5} \frac{\partial}{\partial x} (x^{0.25})

Apply the Power Rule:

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

= y^{0.5} \cdot 0.25 x^{0.25 - 1}

Simplify

y^{\frac{1}{2}} \cdot 0.25 x^{0.25 - 1} : \frac{0.25 y ^{\frac{1}{2}}}{x ^{0.75}}

= \frac{0.25 y ^{\frac{1}{2}}}{x ^{0.75}}

\frac{d y}{d x} = x - 3

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f (x) = x^{2} + 4, (4, 20)

What is (\partial)/(\partial x)(x^{0.25}y^{0.5}) ?
The answer to (\partial)/(\partial x)(x^{0.25}y^{0.5}) is (0.25y^{1/2})/(x^{0.75)}