What is the d/(ds)(((s^2-a^2))/((s^2+s^2)^2)) ?

The d/(ds)(((s^2-a^2))/((s^2+s^2)^2)) is (-s^2+2a^2)/(2s^5)

What is the first d/(ds)(((s^2-a^2))/((s^2+s^2)^2)) ?

The first d/(ds)(((s^2-a^2))/((s^2+s^2)^2)) is (-s^2+2a^2)/(2s^5)

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

\frac{- s ^{2} + 2 a ^{2}}{2 s ^{5}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d s} ((s^{2} + s^{2})^{2}) = 16 s^{3}

= \frac{2 s ( s ^{2} + s ^{2} ) ^{2} - 16 s ^{3} ( s ^{2} - a ^{2} )}{( ( s ^{2} + s ^{2} ) ^{2} ) ^{2}}

Simplify

\frac{2 s ( s ^{2} + s ^{2} ) ^{2} - 16 s ^{3} ( s ^{2} - a ^{2} )}{( ( s ^{2} + s ^{2} ) ^{2} ) ^{2}} : \frac{- s ^{2} + 2 a ^{2}}{2 s ^{5}}

= \frac{- s ^{2} + 2 a ^{2}}{2 s ^{5}}

\frac{d}{d t} (- 20 + 5 t)

y = \frac{1 + x + x ^{2}}{1 - x ^{2}}

\frac{( x ^{4} - 5 )}{( x ^{2} + 3 )}

sec (x) + sin (x) + x^{- 5}

\frac{d}{d a} (sin^{4} (a) - cos^{4} (a) + 1)

What is the d/(ds)(((s^2-a^2))/((s^2+s^2)^2)) ?
The d/(ds)(((s^2-a^2))/((s^2+s^2)^2)) is (-s^2+2a^2)/(2s^5)
What is the first d/(ds)(((s^2-a^2))/((s^2+s^2)^2)) ?
The first d/(ds)(((s^2-a^2))/((s^2+s^2)^2)) is (-s^2+2a^2)/(2s^5)