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

The derivative of s/((s^2+1)^2) is (-3s^2+1)/((s^2+1)^3)

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

The first derivative of s/((s^2+1)^2) is (-3s^2+1)/((s^2+1)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{- 3 s ^{2} + 1}{( s ^{2} + 1 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d s}{d s} = 1

\frac{d}{d s} ((s^{2} + 1)^{2}) = 4 s (s^{2} + 1)

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

Simplify

\frac{1 \cdot ( s ^{2} + 1 ) ^{2} - 4 s ( s ^{2} + 1 ) s}{( ( s ^{2} + 1 ) ^{2} ) ^{2}} : \frac{- 3 s ^{2} + 1}{( s ^{2} + 1 ) ^{3}}

= \frac{- 3 s ^{2} + 1}{( s ^{2} + 1 ) ^{3}}

8 x^{- 1}

2 x^{3} + 3 lo g_{10} (x) + 2 sin (x)

(1 + x^{2}) lo g_{2} (x)

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

\frac{t ^{2}}{3}

What is the derivative of s/((s^2+1)^2) ?
The derivative of s/((s^2+1)^2) is (-3s^2+1)/((s^2+1)^3)
What is the first derivative of s/((s^2+1)^2) ?
The first derivative of s/((s^2+1)^2) is (-3s^2+1)/((s^2+1)^3)