What is (\partial)/(\partial y)(5x^{4/5}y^{1/5}) ?

The answer to (\partial)/(\partial y)(5x^{4/5}y^{1/5}) is ((x^4)/(y^4))^{1/5}

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(\partial)/(\partial y)(5x^{4/5}y^{1/5})

\frac{\partial}{\partial y} (5 x^{\frac{4}{5}} y^{\frac{1}{5}})

(\frac{x ^{4}}{y ^{4}})^{\frac{1}{5}}

Solution steps

\frac{\partial}{\partial y} (5 x^{\frac{4}{5}} y^{\frac{1}{5}})

Treat

x

as a constant

Take the constant out:

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

= 5 x^{\frac{4}{5}} \frac{\partial}{\partial y} (y^{\frac{1}{5}})

Apply the Power Rule:

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

= 5 x^{\frac{4}{5}} \frac{1}{5} y^{\frac{1}{5} - 1}

Simplify

5 x^{\frac{4}{5}} \frac{1}{5} y^{\frac{1}{5} - 1} : (\frac{x ^{4}}{y ^{4}})^{\frac{1}{5}}

= (\frac{x ^{4}}{y ^{4}})^{\frac{1}{5}}

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What is (\partial)/(\partial y)(5x^{4/5}y^{1/5}) ?
The answer to (\partial)/(\partial y)(5x^{4/5}y^{1/5}) is ((x^4)/(y^4))^{1/5}