What is the derivative of e^tsin(6t) ?

The derivative of e^tsin(6t) is e^tsin(6t)+cos(6t)*6e^t

What is the first derivative of e^tsin(6t) ?

The first derivative of e^tsin(6t) is e^tsin(6t)+cos(6t)*6e^t

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derivative of

e^{t} sin (6 t)

e^{t} sin (6 t) + cos (6 t) \cdot 6 e^{t}

Solution steps

\frac{d}{d t} (e^{t} sin (6 t))

Apply the Product Rule:

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

f = e^{t}, g = sin (6 t)

= \frac{d}{d t} (e^{t}) sin (6 t) + \frac{d}{d t} (sin (6 t)) e^{t}

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

\frac{d}{d t} (sin (6 t)) = cos (6 t) \cdot 6

= e^{t} sin (6 t) + cos (6 t) \cdot 6 e^{t}

\frac{d}{d x} (sin (x) x)

f (x) = 7 e^{x} + 4 x, at x = 0

\int 5^{x} e^{- x} d x

\frac{\partial}{\partial x} ((x - a)^{- 1})

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

What is the derivative of e^tsin(6t) ?
The derivative of e^tsin(6t) is e^tsin(6t)+cos(6t)*6e^t
What is the first derivative of e^tsin(6t) ?
The first derivative of e^tsin(6t) is e^tsin(6t)+cos(6t)*6e^t