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

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

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

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{x ^{3}}{( 1 + x ^{2} ) ^{3}} d x

x \to \infty lim (\frac{3 x ^{2} - 2 x - 5}{x - 4})

\frac{\partial}{\partial y} (sin (y) - y sin (x))

x \to \infty lim (\frac{1}{3 x})

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

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