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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\frac{d}{d x} (\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}}

(1 + 2 x) e^{3 x^{2}}

y^{^{''}} - 14 y^{^{'}} + 48 y = 0

\frac{3}{s \cdot ( s + 2 )}

8 x^{2} - 5 x, x^{3} - 8 x + 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)