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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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