What is (\partial)/(\partial t)(y+xcos(t)) ?

The answer to (\partial)/(\partial t)(y+xcos(t)) is -xsin(t)

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(\partial)/(\partial t)(y+xcos(t))

\frac{\partial}{\partial t} (y + x cos (t))

- x sin (t)

Solution steps

\frac{\partial}{\partial t} (y + x cos (t))

Treat

y, x

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial t} (y) + \frac{\partial}{\partial t} (x cos (t))

\frac{\partial}{\partial t} (y) = 0

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

= 0 - x sin (t)

Simplify

= - x sin (t)

What is (\partial)/(\partial t)(y+xcos(t)) ?
The answer to (\partial)/(\partial t)(y+xcos(t)) is -xsin(t)