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}}

\int 9 x e^{(- 3 x)} d x

f (x) = 3 - x^{2}, at x = 4

y^{^{'}} = 5 - 2 y

y^{^{'}} = cos^{2} (y)

y = \frac{x ^{2}}{x + 1}, (2, \frac{4}{3})

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)