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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

= - \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

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

Simplify

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

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