What is (\partial)/(\partial x)((x+y)/(1+y^2)) ?

The answer to (\partial)/(\partial x)((x+y)/(1+y^2)) is 1/(1+y^2)

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(\partial)/(\partial x)((x+y)/(1+y^2))

\frac{\partial}{\partial x} (\frac{x + y}{1 + y ^{2}})

\frac{1}{1 + y ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x + y}{1 + y ^{2}})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{1 + y ^{2}} \frac{\partial}{\partial x} (x + y)

Apply the Sum/Difference Rule:

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

= \frac{1}{1 + y ^{2}} (\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (y))

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

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

= \frac{1}{1 + y ^{2}} (1 + 0)

Simplify

= \frac{1}{1 + y ^{2}}

\int \frac{( ( ln ( x ) ) ^{2} )}{x} d x

x \to 0 lim (2 x^{2} + 3 x + 1)

\frac{d}{d x} (\frac{x ^{7}}{7})

x \to - 1 + lim (\frac{x}{1 + x ^{3}})

f (x) = - 0.04 x^{4} + 4

What is (\partial)/(\partial x)((x+y)/(1+y^2)) ?
The answer to (\partial)/(\partial x)((x+y)/(1+y^2)) is 1/(1+y^2)