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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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