What is (\partial)/(\partial y)(1/(xy^2z)) ?

The answer to (\partial)/(\partial y)(1/(xy^2z)) is -2/(xy^3z)

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(\partial)/(\partial y)(1/(xy^2z))

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

- \frac{2}{x y ^{3} z}

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{x z} (- 2 y^{- 2 - 1}) : - \frac{2}{x y ^{3} z}

= - \frac{2}{x y ^{3} z}

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What is (\partial)/(\partial y)(1/(xy^2z)) ?
The answer to (\partial)/(\partial y)(1/(xy^2z)) is -2/(xy^3z)