What is the derivative of 1/(x^2-5) ?

The derivative of 1/(x^2-5) is -(2x)/((x^2-5)^2)

What is the first derivative of 1/(x^2-5) ?

The first derivative of 1/(x^2-5) is -(2x)/((x^2-5)^2)

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\frac{d}{d x} (\frac{1}{x ^{2} - 5})

- \frac{2 x}{( x ^{2} - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{2} - 5})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{2} - 5)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} - 5 ) ^{2}} \frac{d}{d x} (x^{2} - 5)

= - \frac{1}{( x ^{2} - 5 ) ^{2}} \frac{d}{d x} (x^{2} - 5)

\frac{d}{d x} (x^{2} - 5) = 2 x

= - \frac{1}{( x ^{2} - 5 ) ^{2}} \cdot 2 x

Simplify

- \frac{1}{( x ^{2} - 5 ) ^{2}} \cdot 2 x : - \frac{2 x}{( x ^{2} - 5 ) ^{2}}

= - \frac{2 x}{( x ^{2} - 5 ) ^{2}}

f (x) = (x^{2} + 3) (x^{2} - 3) x^{2}

\int \frac{1}{cos ^{2} ( x ) 1 - tan ^{2} ( x )} d x

y^{^{''}} - 6 y^{^{'}} = 36 t

n = 0 \sum \infty \frac{n !}{2 ^{n}}

x \to - \infty lim (x^{2} e x)

What is the derivative of 1/(x^2-5) ?
The derivative of 1/(x^2-5) is -(2x)/((x^2-5)^2)
What is the first derivative of 1/(x^2-5) ?
The first derivative of 1/(x^2-5) is -(2x)/((x^2-5)^2)