What is the d/(dt)(e^t*sin(t)) ?

The d/(dt)(e^t*sin(t)) is e^tsin(t)+cos(t)e^t

What is the first d/(dt)(e^t*sin(t)) ?

The first d/(dt)(e^t*sin(t)) is e^tsin(t)+cos(t)e^t

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

e^{t} sin (t) + cos (t) e^{t}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= e^{t} sin (t) + cos (t) e^{t}

\frac{\partial}{\partial x} (0.1 \cdot x \cdot y)

\int 3 x e^{- 2 x} d x

\frac{d y}{d x} = (\frac{2 y + 3}{4 x + 5})^{2}

\int \frac{1}{7} x d x

\frac{10 x + 20}{x}

What is the d/(dt)(e^t*sin(t)) ?
The d/(dt)(e^t*sin(t)) is e^tsin(t)+cos(t)e^t
What is the first d/(dt)(e^t*sin(t)) ?
The first d/(dt)(e^t*sin(t)) is e^tsin(t)+cos(t)e^t