What is (\partial)/(\partial t)(e^{-6t}cos(pix)) ?

The answer to (\partial)/(\partial t)(e^{-6t}cos(pix)) is -6e^{-6t}cos(pix)

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(\partial)/(\partial t)(e^{-6t}cos(pix))

\frac{\partial}{\partial t} (e^{- 6 t} cos (π x))

- 6 e^{- 6 t} cos (π x)

Solution steps

\frac{\partial}{\partial t} (e^{- 6 t} cos (π x))

Treat

x

as a constant

Take the constant out:

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

= cos (π x) \frac{\partial}{\partial t} (e^{- 6 t})

Apply the chain rule:

e^{- 6 t} \frac{\partial}{\partial t} (- 6 t)

= e^{- 6 t} \frac{\partial}{\partial t} (- 6 t)

\frac{\partial}{\partial t} (- 6 t) = - 6

= cos (π x) e^{- 6 t} (- 6)

Simplify

= - 6 e^{- 6 t} cos (π x)

What is (\partial)/(\partial t)(e^{-6t}cos(pix)) ?
The answer to (\partial)/(\partial t)(e^{-6t}cos(pix)) is -6e^{-6t}cos(pix)