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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = s^{2}, g = y (s)

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

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

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

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

20 x - 50, y = 0, 2 x^{2}

\int (4 - r^{2}) r d r

f (x) = 9 x

n \to \infty lim (n^{n})

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