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

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

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

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

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

\frac{d y}{d t} - \frac{5}{t} y = t^{5}

\frac{d}{d x} (\frac{- 1 x + 1 + x}{x ^{2} - 1})

\frac{d}{d x} (1 - 5 cos (x))

x \to + 3 lim (6 x^{2})

\frac{d}{d x} (c \cdot x^{2} \cdot e^{\frac{- m x ^{2}}{2 k t}})

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