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

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

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(\partial)/(\partial z)(1/(xyz^2))

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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

x \to 2 lim ((x - 2) (2^{x} - 4))

x^{3^{x}}

\int \frac{( x + 2 ) ^{2}}{x ^{2} + 4} d x

\int \frac{x + 66}{x ^{2} - 36} d x

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