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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

(x^{2} - 3 x + 1) 25 - x^{2}

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\int (2 - 2 x) d x

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

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