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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{d}{d y} (e^{\frac{x}{y}})

x \to 6 lim (- \frac{1}{x - 6})

\frac{d y}{d x} = \frac{x ^{2} + 2 y}{x}

\int (\frac{x + 11}{x - 9}) d x

\int_{0}^{3} f (x) d x

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