What is the d/(dt)(2e^tsin(t)) ?

The d/(dt)(2e^tsin(t)) is 2(e^tsin(t)+cos(t)e^t)

What is the first d/(dt)(2e^tsin(t)) ?

The first d/(dt)(2e^tsin(t)) is 2(e^tsin(t)+cos(t)e^t)

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\frac{d}{d t} (2 e^{t} sin (t))

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

Solution steps

\frac{d}{d t} (2 e^{t} sin (t))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \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)

= 2 (\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)

= 2 (e^{t} sin (t) + cos (t) e^{t})

\int (sec (x) tan^{5} (x))^{2} d x

\frac{d}{d x} ((3 x^{2} - x + 5)^{3})

\int cos^{2} (1) d x

x \to 0 + lim (x e^{\frac{1}{x}})

What is the d/(dt)(2e^tsin(t)) ?
The d/(dt)(2e^tsin(t)) is 2(e^tsin(t)+cos(t)e^t)
What is the first d/(dt)(2e^tsin(t)) ?
The first d/(dt)(2e^tsin(t)) is 2(e^tsin(t)+cos(t)e^t)