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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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\frac{d y}{d x} = (\frac{y ^{3}}{x ^{2}})

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\int - \frac{y ^{2}}{2} d y

\frac{2 x ^{2}}{6 x + 5}

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