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

The answer to (\partial}{\partial x}(\frac{(x+y))/y) is 1/y

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

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

\frac{1}{y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (y) = 0

= \frac{1}{y} (1 + 0)

Simplify

= \frac{1}{y}

y = - 0.0959 x^{2} + 106.83 x + 71149

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What is (\partial}{\partial x}(\frac{(x+y))/y) ?
The answer to (\partial}{\partial x}(\frac{(x+y))/y) is 1/y