What is (\partial)/(\partial x)(xy^{-1}) ?

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

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(\partial)/(\partial x)(xy^{-1})

\frac{\partial}{\partial x} (x y^{- 1})

\frac{1}{y}

Solution steps

\frac{\partial}{\partial x} (x y^{- 1})

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

\frac{\partial}{\partial x} (x) = 1

= y^{- 1} \cdot 1

Simplify

y^{- 1} \cdot 1 : \frac{1}{y}

= \frac{1}{y}

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