What is the d/(dt)(e^t(acos(2t)+cos(2t))) ?

The d/(dt)(e^t(acos(2t)+cos(2t))) is e^t(acos(2t)+cos(2t))+(-2asin(2t)-sin(2t)*2)e^t

What is the first d/(dt)(e^t(acos(2t)+cos(2t))) ?

The first d/(dt)(e^t(acos(2t)+cos(2t))) is e^t(acos(2t)+cos(2t))+(-2asin(2t)-sin(2t)*2)e^t

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

e^{t} (a cos (2 t) + cos (2 t)) + (- 2 a sin (2 t) - sin (2 t) \cdot 2) e^{t}

Solution steps

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

Apply the Product Rule:

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

f = e^{t}, g = a cos (2 t) + cos (2 t)

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

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

\frac{d}{d t} (a cos (2 t) + cos (2 t)) = - 2 a sin (2 t) - sin (2 t) \cdot 2

= e^{t} (a cos (2 t) + cos (2 t)) + (- 2 a sin (2 t) - sin (2 t) \cdot 2) e^{t}

What is the d/(dt)(e^t(acos(2t)+cos(2t))) ?
The d/(dt)(e^t(acos(2t)+cos(2t))) is e^t(acos(2t)+cos(2t))+(-2asin(2t)-sin(2t)*2)e^t
What is the first d/(dt)(e^t(acos(2t)+cos(2t))) ?
The first d/(dt)(e^t(acos(2t)+cos(2t))) is e^t(acos(2t)+cos(2t))+(-2asin(2t)-sin(2t)*2)e^t