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

The answer to (\partial)/(\partial x)(y/((1+x)^2)) is -(2y)/((1+x)^3)

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

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

- \frac{2 y}{( 1 + x ) ^{3}}

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})

Apply the chain rule:

- \frac{2}{( 1 + x ) ^{3}} \frac{\partial}{\partial x} (1 + x)

= - \frac{2}{( 1 + x ) ^{3}} \frac{\partial}{\partial x} (1 + x)

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

= y (- \frac{2}{( 1 + x ) ^{3}} \cdot 1)

Simplify

y (- \frac{2}{( 1 + x ) ^{3}} \cdot 1) : - \frac{2 y}{( 1 + x ) ^{3}}

= - \frac{2 y}{( 1 + x ) ^{3}}

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\frac{\partial}{\partial y} (2 y^{2} x - 3)

What is (\partial)/(\partial x)(y/((1+x)^2)) ?
The answer to (\partial)/(\partial x)(y/((1+x)^2)) is -(2y)/((1+x)^3)