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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

y (- \frac{1}{( 1 + x ^{2} ) ^{2}} \cdot 2 x) : - \frac{2 y x}{( 1 + x ^{2} ) ^{2}}

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

(60 + 2 t)^{\frac{2}{3}}

f (x) = 3^{4 x + 5}

y = - 1 - 8 x^{2}, (- 2, - 33)

f (x) = x^{\frac{2}{5}}

n = 2 \sum \infty \frac{2}{n ( n + 2 )}

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