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

The answer to (\partial)/(\partial t)(e^tcos(t)) is e^tcos(t)-e^tsin(t)

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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\frac{\partial}{\partial x} (ln (x^{2} z^{2}))

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What is (\partial)/(\partial t)(e^tcos(t)) ?
The answer to (\partial)/(\partial t)(e^tcos(t)) is e^tcos(t)-e^tsin(t)