What is the derivative of 1/((s^2+2)) ?

The derivative of 1/((s^2+2)) is -(2s)/((s^2+2)^2)

What is the first derivative of 1/((s^2+2)) ?

The first derivative of 1/((s^2+2)) is -(2s)/((s^2+2)^2)

derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d t} (t^{3} - 6 t^{2} + 9 t)

d er i v a t i v e \frac{( 1 + e ^{x} )}{( 1 - e ^{x} )}

d er i v a t i v e 5 x^{6}

d er i v a t i v e 2 e^{3} t sin (2 t)

d er i v a t i v e tan (e^{s}) in x^{2}

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