What is expand (15+t)^2(dS)/(dt) ?

The solution to expand (15+t)^2(dS)/(dt) is 225(dS)/(dt)+30t(dS)/(dt)+t^2(dS)/(dt)

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expand (15+t)^2(dS)/(dt)

expand

(15 + t)^{2} \frac{d S}{d t}

225 \frac{d S}{d t} + 30 t \frac{d S}{d t} + t^{2} \frac{d S}{d t}

Solution steps

(15 + t)^{2} \frac{d S}{d t}

(15 + t)^{2} = 225 + 30 t + t^{2}

= (t^{2} + 30 t + 225) \frac{d S}{d t}

Distribute parentheses

= \frac{d S}{d t} 225 + \frac{d S}{d t} 30 t + \frac{d S}{d t} t^{2}

= 225 \frac{d S}{d t} + 30 t \frac{d S}{d t} + t^{2} \frac{d S}{d t}

\frac{5000}{s ( s + 380 )}

sin (n (\frac{π}{2} - x))

\frac{π r}{r ( r + 1 ) - 1}

2 e^{t} cos (t) \cdot (e^{t} cos (t) + e^{t} sin (t))

\frac{8 x ^{2} + 36 x + 47}{( 3 x - 1 ) ( x + 2 ) ( 2 x + 3 )}

What is expand (15+t)^2(dS)/(dt) ?
The solution to expand (15+t)^2(dS)/(dt) is 225(dS)/(dt)+30t(dS)/(dt)+t^2(dS)/(dt)