What is the derivative of (1/(1+x))^{-1} ?

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

What is the first derivative of (1/(1+x))^{-1} ?

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

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derivative of

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

1

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= 1

y = 4 sec (2 x)

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

y = \frac{sin ^{3} ( x ) + 4}{3 cos ^{3} ( x )}

2 x^{3} - 2.5 x - 5

y = \frac{1}{( sin ( x ) + cos ( x ) )}

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