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

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

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

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

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

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

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})^{- 1})

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( 9 - x ^{2} ) ^{2}} (- 2 x) : \frac{2 x}{( 9 - x ^{2} ) ^{2}}

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

\int_{0}^{t} e^{- 2 x} d x

\int e^{- s t} (t - 2)^{2} d t

\int_{x}^{y} (t^{2} - 1) d t

f^{^{'}} (x) = x^{- 3} + π x^{2} - 2

f (2) = 10 - 3 x

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