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

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

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

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

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\frac{d}{d t} (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}

400 x^{10} + 40 x^{5} + 1

y^{^{'}} = \frac{4 sec ( y )}{( x - 6 ) ^{2}}

\frac{( x ^{2} - a ) ^{3}}{a x}

(x + x^{- 1})^{3}

f (x) = - x + \frac{1}{x} + 1

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