What is the derivative of f(x)= 1/(x^2-4) ?

The derivative of f(x)= 1/(x^2-4) is -(2x)/((x^2-4)^2)

What is the first derivative of f(x)= 1/(x^2-4) ?

The first derivative of f(x)= 1/(x^2-4) is -(2x)/((x^2-4)^2)

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derivative of

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

- \frac{2 x}{( x ^{2} - 4 ) ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{2} - 4) = 2 x

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

Simplify

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

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

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\frac{d ^{4}}{d x ^{4}} (5 e^{x^{2}})

\frac{d}{d x} (x^{3} - 7 x^{2} + 15 x - 10)

(6 y + 2 t - 9) d t + (8 y + 6 t - 1) d y = 0

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