What is (\partial)/(\partial x)(x^{1/4}y^{1/4}) ?

The answer to (\partial)/(\partial x)(x^{1/4}y^{1/4}) is (y^{1/4})/(4x^{3/4)}

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(\partial)/(\partial x)(x^{1/4}y^{1/4})

\frac{\partial}{\partial x} (x^{\frac{1}{4}} y^{\frac{1}{4}})

\frac{y ^{\frac{1}{4}}}{4 x ^{\frac{3}{4}}}

Solution steps

\frac{\partial}{\partial x} (x^{\frac{1}{4}} y^{\frac{1}{4}})

Treat

y

as a constant

Take the constant out:

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

= y^{\frac{1}{4}} \frac{\partial}{\partial x} (x^{\frac{1}{4}})

Apply the Power Rule:

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

= y^{\frac{1}{4}} \frac{1}{4} x^{\frac{1}{4} - 1}

Simplify

y^{\frac{1}{4}} \frac{1}{4} x^{\frac{1}{4} - 1} : \frac{y ^{\frac{1}{4}}}{4 x ^{\frac{3}{4}}}

= \frac{y ^{\frac{1}{4}}}{4 x ^{\frac{3}{4}}}

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x \to \infty lim (20)

y = \frac{1}{x ^{2}}, (- 2, \frac{1}{4})

x \to - \infty lim (3^{5 x})

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What is (\partial)/(\partial x)(x^{1/4}y^{1/4}) ?
The answer to (\partial)/(\partial x)(x^{1/4}y^{1/4}) is (y^{1/4})/(4x^{3/4)}