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

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

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

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

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

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

Solution steps

\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{d}{d x} (3 x^{2} + \frac{4 x}{3} - 2)

\frac{( y ^{^{'}} - e ^{- t} + 5 )}{y} = - 5

f (x) = 9 - x

\int 12 x^{5} y^{4} + 15 x^{4} y^{5}

ln (e + x^{2})

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