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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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