What is the d/(dt)(e^{2t}+2e^t+1) ?

The d/(dt)(e^{2t}+2e^t+1) is 2e^t+2e^{2t}

What is the first d/(dt)(e^{2t}+2e^t+1) ?

The first d/(dt)(e^{2t}+2e^t+1) is 2e^t+2e^{2t}

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

2 e^{t} + 2 e^{2 t}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d t} (e^{2 t}) = e^{2 t} \cdot 2

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

\frac{d}{d t} (1) = 0

= e^{2 t} \cdot 2 + 2 e^{t} + 0

Simplify

= 2 e^{t} + 2 e^{2 t}

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What is the d/(dt)(e^{2t}+2e^t+1) ?
The d/(dt)(e^{2t}+2e^t+1) is 2e^t+2e^{2t}
What is the first d/(dt)(e^{2t}+2e^t+1) ?
The first d/(dt)(e^{2t}+2e^t+1) is 2e^t+2e^{2t}