What is (\partial)/(\partial y)(1/(xy)) ?

The answer to (\partial)/(\partial y)(1/(xy)) is -1/(xy^2)

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(\partial)/(\partial y)(1/(xy))

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

- \frac{1}{x y ^{2}}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{x} (- 1 \cdot y^{- 1 - 1}) : - \frac{1}{x y ^{2}}

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

y^{^{'}} = \frac{15 x}{y}

\int e^{x (t - 1)} d x

\frac{\partial}{\partial x} (arctan (x))

\frac{1}{s ^{2} + s ( \frac{3}{2} ) 2}

\int \frac{1}{7 x} d x

What is (\partial)/(\partial y)(1/(xy)) ?
The answer to (\partial)/(\partial y)(1/(xy)) is -1/(xy^2)