What is (\partial)/(\partial t)(sin(x)cos(ct)) ?

The answer to (\partial)/(\partial t)(sin(x)cos(ct)) is -csin(ct)sin(x)

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(\partial)/(\partial t)(sin(x)cos(ct))

\frac{\partial}{\partial t} (sin (x) cos (c t))

- c sin (c t) sin (x)

Solution steps

\frac{\partial}{\partial t} (sin (x) cos (c t))

Treat

c, x

as a constant

Take the constant out:

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

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

Apply the chain rule:

- sin (c t) \frac{\partial}{\partial t} (c t)

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

\frac{\partial}{\partial t} (c t) = c

= sin (x) (- sin (c t) c)

Simplify

= - c sin (c t) sin (x)

What is (\partial)/(\partial t)(sin(x)cos(ct)) ?
The answer to (\partial)/(\partial t)(sin(x)cos(ct)) is -csin(ct)sin(x)