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Popular >

derivative of e^{13t}cos(t)

Solution

derivative of

e^{13 t} cos (t)

Solution

13 e^{13 t} cos (t) - e^{13 t} sin (t)

Solution steps

\frac{d}{d t} (e^{13 t} cos (t))

Apply the Product Rule:

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

f = e^{13 t}, g = cos (t)

= \frac{d}{d t} (e^{13 t}) cos (t) + \frac{d}{d t} (cos (t)) e^{13 t}

\frac{d}{d t} (e^{13 t}) = e^{13 t} \cdot 13

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

= e^{13 t} \cdot 13 cos (t) + (- sin (t)) e^{13 t}

Simplify

= 13 e^{13 t} cos (t) - e^{13 t} sin (t)

Popular Examples

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x \to 0 lim (x^{21 x})

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\int sin (16 x) cos (11 x) d x

\frac{d N}{d t} = 5 - N

Frequently Asked Questions (FAQ)

What is the derivative of e^{13t}cos(t) ?
The derivative of e^{13t}cos(t) is 13e^{13t}cos(t)-e^{13t}sin(t)
What is the first derivative of e^{13t}cos(t) ?
The first derivative of e^{13t}cos(t) is 13e^{13t}cos(t)-e^{13t}sin(t)