What is (\partial)/(\partial x)(x^{3/4}y^{-4}) ?

The answer to (\partial)/(\partial x)(x^{3/4}y^{-4}) is 3/(4y^4x^{1/4)}

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(\partial)/(\partial x)(x^{3/4}y^{-4})

\frac{\partial}{\partial x} (x^{\frac{3}{4}} y^{- 4})

\frac{3}{4 y ^{4} x ^{\frac{1}{4}}}

Solution steps

\frac{\partial}{\partial x} (x^{\frac{3}{4}} y^{- 4})

Treat

y

as a constant

Take the constant out:

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

= y^{- 4} \frac{\partial}{\partial x} (x^{\frac{3}{4}})

Apply the Power Rule:

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

= y^{- 4} \frac{3}{4} x^{\frac{3}{4} - 1}

Simplify

y^{- 4} \frac{3}{4} x^{\frac{3}{4} - 1} : \frac{3}{4 y ^{4} x ^{\frac{1}{4}}}

= \frac{3}{4 y ^{4} x ^{\frac{1}{4}}}

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What is (\partial)/(\partial x)(x^{3/4}y^{-4}) ?
The answer to (\partial)/(\partial x)(x^{3/4}y^{-4}) is 3/(4y^4x^{1/4)}