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Popular >

derivative of e^{3t}cos(3t)

Solution

derivative of

e^{3 t} cos (3 t)

Solution

3 e^{3 t} cos (3 t) - 3 e^{3 t} sin (3 t)

Solution steps

\frac{d}{d t} (e^{3 t} cos (3 t))

Apply the Product Rule:

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

f = e^{3 t}, g = cos (3 t)

= \frac{d}{d t} (e^{3 t}) cos (3 t) + \frac{d}{d t} (cos (3 t)) e^{3 t}

\frac{d}{d t} (e^{3 t}) = e^{3 t} \cdot 3

\frac{d}{d t} (cos (3 t)) = - sin (3 t) \cdot 3

= e^{3 t} \cdot 3 cos (3 t) + (- sin (3 t) \cdot 3) e^{3 t}

Simplify

= 3 e^{3 t} cos (3 t) - 3 e^{3 t} sin (3 t)

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\int_{\frac{1}{2}}^{4} \frac{2}{x} - \frac{1}{8} x d x

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\frac{d}{d x} (\frac{2 x}{e ^{x}})

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Frequently Asked Questions (FAQ)

What is the derivative of e^{3t}cos(3t) ?
The derivative of e^{3t}cos(3t) is 3e^{3t}cos(3t)-3e^{3t}sin(3t)
What is the first derivative of e^{3t}cos(3t) ?
The first derivative of e^{3t}cos(3t) is 3e^{3t}cos(3t)-3e^{3t}sin(3t)