What is (\partial)/(\partial t)(e^tsin(t)) ?

The answer to (\partial)/(\partial t)(e^tsin(t)) is e^tsin(t)+cos(t)e^t

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(\partial)/(\partial t)(e^tsin(t))

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

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

Solution steps

\frac{\partial}{\partial 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{\partial}{\partial t} (e^{t}) sin (t) + \frac{\partial}{\partial t} (sin (t)) e^{t}

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

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

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

\frac{d}{d x} (3 ln (4 x))

\int_{1}^{3} (4 x - 3)^{2} - (x^{2})^{2} d x

\int \frac{6 x ^{2} + 8}{x ^{3} + 4 x} d x

\frac{d y}{d x} + \frac{1}{x} y = x y^{2}

\frac{d y}{d x} + y = e^{7 x}

What is (\partial)/(\partial t)(e^tsin(t)) ?
The answer to (\partial)/(\partial t)(e^tsin(t)) is e^tsin(t)+cos(t)e^t