What is the d/(dt)({v}(t)t) ?

The d/(dt)({v}(t)t) is t d/(dt)({v}(t))+{v}(t)

What is the first d/(dt)({v}(t)t) ?

The first d/(dt)({v}(t)t) is t d/(dt)({v}(t))+{v}(t)

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

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

Solution steps

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

Apply the Product Rule:

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

f = v (t), g = t

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

\frac{d t}{d t} = 1

= \frac{d}{d t} (v (t)) t + 1 \cdot v (t)

Simplify

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

\frac{\partial}{\partial x} (x^{2} - 2 x y)

\frac{\partial}{\partial x} (y^{2} x)

\int \frac{4 + x ^{2}}{x} d x

x \to - 3 lim (x^{2} - 9)

x \to 7 - lim (\frac{2}{x + 7})

What is the d/(dt)({v}(t)t) ?
The d/(dt)({v}(t)t) is t d/(dt)({v}(t))+{v}(t)
What is the first d/(dt)({v}(t)t) ?
The first d/(dt)({v}(t)t) is t d/(dt)({v}(t))+{v}(t)