What is the derivative of e^tsin(4t) ?

The derivative of e^tsin(4t) is e^tsin(4t)+cos(4t)*4e^t

What is the first derivative of e^tsin(4t) ?

The first derivative of e^tsin(4t) is e^tsin(4t)+cos(4t)*4e^t

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derivative of

e^{t} sin (4 t)

e^{t} sin (4 t) + cos (4 t) \cdot 4 e^{t}

Solution steps

\frac{d}{d t} (e^{t} sin (4 t))

Apply the Product Rule:

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

f = e^{t}, g = sin (4 t)

= \frac{d}{d t} (e^{t}) sin (4 t) + \frac{d}{d t} (sin (4 t)) e^{t}

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

\frac{d}{d t} (sin (4 t)) = cos (4 t) \cdot 4

= e^{t} sin (4 t) + cos (4 t) \cdot 4 e^{t}

\int sin^{5} (2 x) cos (2 x) d x

\int \frac{2 x + 1}{x ^{2} + 2 x - 3} d x

\int e^{- 2 k x} d x

y = 7 + 9 x

\frac{d}{d x} (5 sec (x) - 10 cos (x))

What is the derivative of e^tsin(4t) ?
The derivative of e^tsin(4t) is e^tsin(4t)+cos(4t)*4e^t
What is the first derivative of e^tsin(4t) ?
The first derivative of e^tsin(4t) is e^tsin(4t)+cos(4t)*4e^t