What is (\partial)/(\partial t)(sin(x-at)) ?

The answer to (\partial)/(\partial t)(sin(x-at)) is -acos(x-at)

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(\partial)/(\partial t)(sin(x-at))

\frac{\partial}{\partial t} (sin (x - a t))

- a cos (x - a t)

Solution steps

\frac{\partial}{\partial t} (sin (x - a t))

Treat

a, x

as a constant

Apply the chain rule:

cos (x - a t) \frac{\partial}{\partial t} (x - a t)

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

\frac{\partial}{\partial t} (x - a t) = - a

= cos (x - a t) (- a)

Simplify

= - a cos (x - a t)

cos (2 t) (1 + e^{- 3 t})

\frac{d}{d x} ((x^{3} + 1)^{5})

\frac{\partial}{\partial x} (e^{- \frac{1}{x}})

- 3 x^{2} y + y^{^{'}} = - 9 x^{2}

\int_{- 8}^{0} 2 + 64 - x^{2} d x

What is (\partial)/(\partial t)(sin(x-at)) ?
The answer to (\partial)/(\partial t)(sin(x-at)) is -acos(x-at)