What is the derivative of (x^2+2)^{-1} ?

The derivative of (x^2+2)^{-1} is -(2x)/((x^2+2)^2)

What is the first derivative of (x^2+2)^{-1} ?

The first derivative of (x^2+2)^{-1} is -(2x)/((x^2+2)^2)

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derivative of

(x^{2} + 2)^{- 1}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{1}{( 1 + e ^{u} )}

ln ((1 + 3 x)^{2})

3 t + 4

3 t - 1

\frac{3}{x ^{2} + 2}

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