What is (\partial)/(\partial x)(5x^{0.75}y^{0.25}) ?

The answer to (\partial)/(\partial x)(5x^{0.75}y^{0.25}) is (3.75y^{0.25})/(x^{0.25)}

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(\partial)/(\partial x)(5x^{0.75}y^{0.25})

\frac{\partial}{\partial x} (5 x^{0.75} y^{0.25})

\frac{3.75 y ^{0.25}}{x ^{0.25}}

Solution steps

\frac{\partial}{\partial x} (5 x^{0.75} y^{0.25})

Treat

y

as a constant

Take the constant out:

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

= 5 y^{0.25} \frac{\partial}{\partial x} (x^{0.75})

Apply the Power Rule:

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

= 5 y^{0.25} \cdot 0.75 x^{0.75 - 1}

Simplify

5 y^{0.25} \cdot 0.75 x^{0.75 - 1} : \frac{3.75 y ^{0.25}}{x ^{0.25}}

= \frac{3.75 y ^{0.25}}{x ^{0.25}}

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\int_{- \infty}^{- 1} e^{- 20 t} d t

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What is (\partial)/(\partial x)(5x^{0.75}y^{0.25}) ?
The answer to (\partial)/(\partial x)(5x^{0.75}y^{0.25}) is (3.75y^{0.25})/(x^{0.25)}