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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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