What is the d/(dt)(y+{v}(t)*t+(a/2)*t^2) ?

The d/(dt)(y+{v}(t)*t+(a/2)*t^2) is (dy)/(dt)+{v}(t)+t d/(dt)({v}(t))+at

What is the first d/(dt)(y+{v}(t)*t+(a/2)*t^2) ?

The first d/(dt)(y+{v}(t)*t+(a/2)*t^2) is (dy)/(dt)+{v}(t)+t d/(dt)({v}(t))+at

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\frac{d}{d t} (y + v (t) \cdot t + (\frac{a}{2}) \cdot t^{2})

\frac{d y}{d t} + v (t) + t \frac{d}{d t} (v (t)) + a t

Solution steps

\frac{d}{d t} (y + v (t) t + (\frac{a}{2}) t^{2})

Simplify

y + v (t) t + (\frac{a}{2}) t^{2} : y + t v (t) + \frac{a t ^{2}}{2}

= \frac{d}{d t} (y + t v (t) + \frac{a t ^{2}}{2})

Apply the Sum/Difference Rule:

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

= \frac{d y}{d t} + \frac{d}{d t} (t v (t)) + \frac{d}{d t} (\frac{a t ^{2}}{2})

\frac{d}{d t} (t v (t)) = v (t) + t \frac{d}{d t} (v (t))

\frac{d}{d t} (\frac{a t ^{2}}{2}) = a t

= \frac{d y}{d t} + v (t) + t \frac{d}{d t} (v (t)) + a t

\int_{0}^{2} x 2 - x d x

\frac{d}{d x} ((8 x + 5) (x^{2} - 3 x))

\frac{d}{d x} (\frac{e ^{x}}{1 + x ^{2}})

\int_{1}^{6} \frac{2}{x ^{3}} d x

6 - 4 x^{2}

What is the d/(dt)(y+{v}(t)*t+(a/2)*t^2) ?
The d/(dt)(y+{v}(t)*t+(a/2)*t^2) is (dy)/(dt)+{v}(t)+t d/(dt)({v}(t))+at
What is the first d/(dt)(y+{v}(t)*t+(a/2)*t^2) ?
The first d/(dt)(y+{v}(t)*t+(a/2)*t^2) is (dy)/(dt)+{v}(t)+t d/(dt)({v}(t))+at