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}}

\frac{\partial}{\partial x} (x^{2} - 2 x^{2} y - 5 x y^{2})

\int (2 x)^{2} (5 + 3^{4})^{\frac{1}{4}} d x

tan (2 x + 5)

\int 2 + tan^{2} (x) d x

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