What is (\partial)/(\partial y)(-1/(x^2y)) ?

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

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(\partial)/(\partial y)(-1/(x^2y))

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= - \frac{1}{x ^{2}} \frac{\partial}{\partial y} (\frac{1}{y})

Apply exponent rule:

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

= - \frac{1}{x ^{2}} \frac{\partial}{\partial y} (y^{- 1})

Apply the Power Rule:

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

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

Simplify

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

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

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