What is the derivative of 1/((9+x^2)) ?

The derivative of 1/((9+x^2)) is -2/((9+x)^3)

What is the first derivative of 1/((9+x^2)) ?

The first derivative of 1/((9+x^2)) is -2/((9+x)^3)

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\frac{d}{d x} (\frac{1}{( 9 + x ) ^{2}})

- \frac{2}{( 9 + x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{1}{( 9 + x ) ^{2}})

Apply exponent rule:

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

= \frac{d}{d x} ((9 + x)^{- 2})

Apply the chain rule:

- \frac{2}{( 9 + x ) ^{3}} \frac{d}{d x} (9 + x)

= - \frac{2}{( 9 + x ) ^{3}} \frac{d}{d x} (9 + x)

\frac{d}{d x} (9 + x) = 1

= - \frac{2}{( 9 + x ) ^{3}} \cdot 1

Simplify

= - \frac{2}{( 9 + x ) ^{3}}

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What is the derivative of 1/((9+x^2)) ?
The derivative of 1/((9+x^2)) is -2/((9+x)^3)
What is the first derivative of 1/((9+x^2)) ?
The first derivative of 1/((9+x^2)) is -2/((9+x)^3)