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

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

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

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

\frac{1}{1 + x}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= \frac{1}{1 + x}

\frac{\partial}{\partial x} (\frac{a}{sin ( x )})

y^{^{'}} + y cos (x) = 5 cos (x), y (0) = 7

x \to 1 - lim (3 x - 5)

\int x (- 1 + x^{2}) d x

x \to 0 lim (\frac{4 x - sin ( x )}{x})

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