What is the derivative of e^tcos(6t) ?

The derivative of e^tcos(6t) is e^tcos(6t)-6e^tsin(6t)

What is the first derivative of e^tcos(6t) ?

The first derivative of e^tcos(6t) is e^tcos(6t)-6e^tsin(6t)

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derivative of

e^{t} cos (6 t)

e^{t} cos (6 t) - 6 e^{t} sin (6 t)

Solution steps

\frac{d}{d t} (e^{t} cos (6 t))

Apply the Product Rule:

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

f = e^{t}, g = cos (6 t)

= \frac{d}{d t} (e^{t}) cos (6 t) + \frac{d}{d t} (cos (6 t)) e^{t}

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

\frac{d}{d t} (cos (6 t)) = - sin (6 t) \cdot 6

= e^{t} cos (6 t) + (- sin (6 t) \cdot 6) e^{t}

Simplify

= e^{t} cos (6 t) - 6 e^{t} sin (6 t)

What is the derivative of e^tcos(6t) ?
The derivative of e^tcos(6t) is e^tcos(6t)-6e^tsin(6t)
What is the first derivative of e^tcos(6t) ?
The first derivative of e^tcos(6t) is e^tcos(6t)-6e^tsin(6t)