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

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

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

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

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derivative of

e^{t} 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}

f (t) = t^{2} + 1

n = 8 \sum \infty e^{5 - 6 n}

\int_{0}^{\frac{3}{2}} cos (π x) d x

y^{^{'}} = e^{x}

\frac{\partial}{\partial y} (\frac{4 y}{x})

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