What is (\partial)/(\partial x)(x^{0.2}*y^{0.8}) ?

The answer to (\partial)/(\partial x)(x^{0.2}*y^{0.8}) is (0.2y^{0.8})/(x^{0.8)}

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(\partial)/(\partial x)(x^{0.2}*y^{0.8})

\frac{\partial}{\partial x} (x^{0.2} \cdot y^{0.8})

\frac{0.2 y ^{0.8}}{x ^{0.8}}

Solution steps

\frac{\partial}{\partial x} (x^{0.2} y^{0.8})

Treat

y

as a constant

Take the constant out:

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

= y^{0.8} \frac{\partial}{\partial x} (x^{0.2})

Apply the Power Rule:

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

= y^{0.8} \cdot 0.2 x^{0.2 - 1}

Simplify

y^{0.8} \cdot 0.2 x^{0.2 - 1} : \frac{0.2 y ^{0.8}}{x ^{0.8}}

= \frac{0.2 y ^{0.8}}{x ^{0.8}}

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What is (\partial)/(\partial x)(x^{0.2}*y^{0.8}) ?
The answer to (\partial)/(\partial x)(x^{0.2}*y^{0.8}) is (0.2y^{0.8})/(x^{0.8)}