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

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

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

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

\frac{1}{z}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= \frac{1}{z}

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(- \frac{4}{3}) \cdot e^{- 2 t} + (- \frac{2}{3}) \cdot e^{t}

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