What is the d/(dt)((c_{1}+c,t)*e^t) ?

The d/(dt)((c_{1}+c,t)*e^t) is (0+(c,1))e^t+e^t(c_{1}+c,t)

What is the first d/(dt)((c_{1}+c,t)*e^t) ?

The first d/(dt)((c_{1}+c,t)*e^t) is (0+(c,1))e^t+e^t(c_{1}+c,t)

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\frac{d}{d t} ((c_{1} + c, t) \cdot e^{t})

(0 + (c, 1)) e^{t} + e^{t} (c_{1} + c, t)

Solution steps

\frac{d}{d t} ((c_{1} + c, t) e^{t})

Apply the Product Rule:

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

f = c_{1} + c, t, g = e^{t}

= \frac{d}{d t} (c_{1} + c, t) e^{t} + \frac{d}{d t} (e^{t}) (c_{1} + c, t)

\frac{d}{d t} (c_{1} + c, t) = 0 + (c, 1)

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

= (0 + (c, 1)) e^{t} + e^{t} (c_{1} + c, t)

What is the d/(dt)((c_{1}+c,t)*e^t) ?
The d/(dt)((c_{1}+c,t)*e^t) is (0+(c,1))e^t+e^t(c_{1}+c,t)
What is the first d/(dt)((c_{1}+c,t)*e^t) ?
The first d/(dt)((c_{1}+c,t)*e^t) is (0+(c,1))e^t+e^t(c_{1}+c,t)