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) = - 16 t^{2}

\frac{s - 1}{2 ( s ^{2} + 1 )}

2 x^{2} - 5 x + 3

sin (x - x^{2})

\frac{d}{d x} (2^{2^{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)