What is the d/(dt)({v}(t)e^{0.1t}) ?

The d/(dt)({v}(t)e^{0.1t}) is d/(dt)({v}(t))e^{0.1t}+e^{0.1t}*0.1{v}(t)

What is the first d/(dt)({v}(t)e^{0.1t}) ?

The first d/(dt)({v}(t)e^{0.1t}) is d/(dt)({v}(t))e^{0.1t}+e^{0.1t}*0.1{v}(t)

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\frac{d}{d t} (v (t) e^{0.1 t})

\frac{d}{d t} (v (t)) e^{0.1 t} + e^{0.1 t} \cdot 0.1 v (t)

Solution steps

\frac{d}{d t} (v (t) e^{0.1 t})

Apply the Product Rule:

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

f = v (t), g = e^{0.1 t}

= \frac{d}{d t} (v (t)) e^{0.1 t} + \frac{d}{d t} (e^{0.1 t}) v (t)

\frac{d}{d t} (e^{0.1 t}) = e^{0.1 t} \cdot 0.1

= \frac{d}{d t} (v (t)) e^{0.1 t} + e^{0.1 t} \cdot 0.1 v (t)

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What is the d/(dt)({v}(t)e^{0.1t}) ?
The d/(dt)({v}(t)e^{0.1t}) is d/(dt)({v}(t))e^{0.1t}+e^{0.1t}*0.1{v}(t)
What is the first d/(dt)({v}(t)e^{0.1t}) ?
The first d/(dt)({v}(t)e^{0.1t}) is d/(dt)({v}(t))e^{0.1t}+e^{0.1t}*0.1{v}(t)