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Popular >

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

Solution

derivative of

e^{3 t} sin (3 t)

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

\frac{d y}{d x} - 2 = - y

d/(dy)(ycos(y))

\frac{d}{d y} (y cos (y))

derivative of f(x)=(x^2)/(x-6)derivative of

f (x) = \frac{x ^{2}}{x - 6}

integral of sin^2(1/4 x)

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

x*(dy)/(dx)+y=-6xy^2,y(1)=-7

x \cdot \frac{d y}{d x} + y = - 6 x y^{2}, y (1) = - 7

Frequently Asked Questions (FAQ)

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