What is (\partial)/(\partial x)((x+y)/(y+1)) ?

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

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(\partial)/(\partial x)((x+y)/(y+1))

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

\frac{1}{y + 1}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

Simplify

= \frac{1}{y + 1}

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