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Popular >

d/(dt)(e^{3it})

Solution

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

Solution

- sin (3 t) \cdot 3 + i cos (3 t) \cdot 3

Solution steps

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

Simplify

e^{3 i t} : cos (3 t) + i sin (3 t)

= \frac{d}{d t} (cos (3 t) + i sin (3 t))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (cos (3 t)) + \frac{d}{d t} (i sin (3 t))

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

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

= - sin (3 t) \cdot 3 + i cos (3 t) \cdot 3

Popular Examples

integral of (x^3)/(x^2-100)

\int \frac{x ^{3}}{x ^{2} - 100} d x

sum from n=1 to infinity of 2/(n^2+4n+2)

n = 1 \sum \infty \frac{2}{n ^{2} + 4 n + 2}

derivative of (sin(5x)/(cos(6x)))

\frac{d}{d x} (\frac{sin ( 5 x )}{cos ( 6 x )})

derivative of (x^2-4^2(x-1))

\frac{d}{d x} ((x^{2} - 4)^{2} (x - 1))

derivative of ((1-5t))/(2+t)derivative of

\frac{( 1 - 5 t )}{2 + t}

Frequently Asked Questions (FAQ)

What is the d/(dt)(e^{3it}) ?
The d/(dt)(e^{3it}) is -sin(3t)*3+icos(3t)*3
What is the first d/(dt)(e^{3it}) ?
The first d/(dt)(e^{3it}) is -sin(3t)*3+icos(3t)*3