What is the derivative of 1/(x^2+18x+88) ?

The derivative of 1/(x^2+18x+88) is -(2x+18)/((x^2+18x+88)^2)

What is the first derivative of 1/(x^2+18x+88) ?

The first derivative of 1/(x^2+18x+88) is -(2x+18)/((x^2+18x+88)^2)

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derivative of

\frac{1}{x ^{2} + 18 x + 88}

- \frac{2 x + 18}{( x ^{2} + 18 x + 88 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{2} + 18 x + 88})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{2} + 18 x + 88)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} + 18 x + 88 ) ^{2}} \frac{d}{d x} (x^{2} + 18 x + 88)

= - \frac{1}{( x ^{2} + 18 x + 88 ) ^{2}} \frac{d}{d x} (x^{2} + 18 x + 88)

\frac{d}{d x} (x^{2} + 18 x + 88) = 2 x + 18

= - \frac{1}{( x ^{2} + 18 x + 88 ) ^{2}} (2 x + 18)

Simplify

- \frac{1}{( x ^{2} + 18 x + 88 ) ^{2}} (2 x + 18) : - \frac{2 x + 18}{( x ^{2} + 18 x + 88 ) ^{2}}

= - \frac{2 x + 18}{( x ^{2} + 18 x + 88 ) ^{2}}

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What is the derivative of 1/(x^2+18x+88) ?
The derivative of 1/(x^2+18x+88) is -(2x+18)/((x^2+18x+88)^2)
What is the first derivative of 1/(x^2+18x+88) ?
The first derivative of 1/(x^2+18x+88) is -(2x+18)/((x^2+18x+88)^2)