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

The derivative of (x+1^{-2}) is -2/((x+1)^3)

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

The first derivative of (x+1^{-2}) is -2/((x+1)^3)

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

- \frac{2}{( x + 1 ) ^{3}}

Solution steps

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

Apply the chain rule:

- \frac{2}{( x + 1 ) ^{3}} \frac{d}{d x} (x + 1)

= - \frac{2}{( x + 1 ) ^{3}} \frac{d}{d x} (x + 1)

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

= - \frac{2}{( x + 1 ) ^{3}} \cdot 1

Simplify

= - \frac{2}{( x + 1 ) ^{3}}

y^{^{''}} + 4 y^{^{'}} + 5 y = 5 x + 5 e^{- x}

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What is the derivative of (x+1^{-2}) ?
The derivative of (x+1^{-2}) is -2/((x+1)^3)
What is the first derivative of (x+1^{-2}) ?
The first derivative of (x+1^{-2}) is -2/((x+1)^3)