What is (\partial}{\partial z}(\frac{(7x+7y))/z) ?

The answer to (\partial}{\partial z}(\frac{(7x+7y))/z) is -(7x+7y)/(z^2)

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(\partial}{\partial z}(\frac{(7x+7y))/z)

\frac{\partial}{\partial z} (\frac{( 7 x + 7 y )}{z})

- \frac{7 x + 7 y}{z ^{2}}

Solution steps

\frac{\partial}{\partial z} (\frac{( 7 x + 7 y )}{z})

Treat

x, y

as constants

Take the constant out:

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

= (7 x + 7 y) \frac{\partial}{\partial z} (\frac{1}{z})

Apply exponent rule:

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

= (7 x + 7 y) \frac{\partial}{\partial z} (z^{- 1})

Apply the Power Rule:

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

= (7 x + 7 y) (- 1 \cdot z^{- 1 - 1})

Simplify

(7 x + 7 y) (- 1 \cdot z^{- 1 - 1}) : - \frac{7 x + 7 y}{z ^{2}}

= - \frac{7 x + 7 y}{z ^{2}}

\frac{d}{d x} (- 9 x)

x \to - 3 lim (\frac{x ^{2} - 1}{3 - x})

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

x \to 0 + lim ((4 x)^{\frac{3}{x}})

\frac{5 x ^{4} + x ^{2}}{2}

What is (\partial}{\partial z}(\frac{(7x+7y))/z) ?
The answer to (\partial}{\partial z}(\frac{(7x+7y))/z) is -(7x+7y)/(z^2)