What is (\partial)/(\partial x)(x^{2/5}*y^{3/5}) ?

The answer to (\partial)/(\partial x)(x^{2/5}*y^{3/5}) is (2y^{3/5})/(5x^{3/5)}

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(\partial)/(\partial x)(x^{2/5}*y^{3/5})

\frac{\partial}{\partial x} (x^{\frac{2}{5}} \cdot y^{\frac{3}{5}})

\frac{2 y ^{\frac{3}{5}}}{5 x ^{\frac{3}{5}}}

Solution steps

\frac{\partial}{\partial x} (x^{\frac{2}{5}} y^{\frac{3}{5}})

Treat

y

as a constant

Take the constant out:

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

= y^{\frac{3}{5}} \frac{\partial}{\partial x} (x^{\frac{2}{5}})

Apply the Power Rule:

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

= y^{\frac{3}{5}} \frac{2}{5} x^{\frac{2}{5} - 1}

Simplify

y^{\frac{3}{5}} \frac{2}{5} x^{\frac{2}{5} - 1} : \frac{2 y ^{\frac{3}{5}}}{5 x ^{\frac{3}{5}}}

= \frac{2 y ^{\frac{3}{5}}}{5 x ^{\frac{3}{5}}}

What is (\partial)/(\partial x)(x^{2/5}*y^{3/5}) ?
The answer to (\partial)/(\partial x)(x^{2/5}*y^{3/5}) is (2y^{3/5})/(5x^{3/5)}