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Popular Calculus >

derivative of 1/((1+x^2^2))

Solution

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

Solution

- \frac{4 x}{( 1 + x ^{2} ) ^{3}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{2}{( 1 + x ^{2} ) ^{3}} \cdot 2 x : - \frac{4 x}{( 1 + x ^{2} ) ^{3}}

= - \frac{4 x}{( 1 + x ^{2} ) ^{3}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 1/((1+x^2^2)) ?
The derivative of 1/((1+x^2^2)) is -(4x)/((1+x^2)^3)
What is the first derivative of 1/((1+x^2^2)) ?
The first derivative of 1/((1+x^2^2)) is -(4x)/((1+x^2)^3)