What is the derivative of 1/((1+x)) ?

The derivative of 1/((1+x)) is -1/((1+x)^2)

What is the first derivative of 1/((1+x)) ?

The first derivative of 1/((1+x)) is -1/((1+x)^2)

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x^{6} + x^{3} + 2

\frac{5 x}{2}

\frac{x - 1}{x}

1 - 2 x y

What is the derivative of 1/((1+x)) ?
The derivative of 1/((1+x)) is -1/((1+x)^2)
What is the first derivative of 1/((1+x)) ?
The first derivative of 1/((1+x)) is -1/((1+x)^2)