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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int \frac{x}{x ^{3}} d x

\int_{2}^{3} \frac{24}{3 - x} d x

f (x) = \frac{5}{ln ( x )}

\frac{d}{d x} ((x - a)^{3})

\int \frac{sin ( \frac{1}{x ^{2}} )}{x ^{3}} d x

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