What is the d/(ds)(s^2{y}(s)-1) ?

The d/(ds)(s^2{y}(s)-1) is s^2 d/(ds)({y}(s))+2s{y}(s)

What is the first d/(ds)(s^2{y}(s)-1) ?

The first d/(ds)(s^2{y}(s)-1) is s^2 d/(ds)({y}(s))+2s{y}(s)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d s} (1) = 0

= 2 s y (s) + \frac{d}{d s} (y (s)) s^{2} - 0

Simplify

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

What is the d/(ds)(s^2{y}(s)-1) ?
The d/(ds)(s^2{y}(s)-1) is s^2 d/(ds)({y}(s))+2s{y}(s)
What is the first d/(ds)(s^2{y}(s)-1) ?
The first d/(ds)(s^2{y}(s)-1) is s^2 d/(ds)({y}(s))+2s{y}(s)