What is (\partial)/(\partial t)(e^{-2x}cos(9pit)) ?

The answer to (\partial)/(\partial t)(e^{-2x}cos(9pit)) is -9pie^{-2x}sin(9pit)

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(\partial)/(\partial t)(e^{-2x}cos(9pit))

\frac{\partial}{\partial t} (e^{- 2 x} cos (9 π t))

- 9 π e^{- 2 x} sin (9 π t)

Solution steps

\frac{\partial}{\partial t} (e^{- 2 x} cos (9 π t))

Treat

x

as a constant

Take the constant out:

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

= e^{- 2 x} \frac{\partial}{\partial t} (cos (9 π t))

Apply the chain rule:

- sin (9 π t) \frac{\partial}{\partial t} (9 π t)

= - sin (9 π t) \frac{\partial}{\partial t} (9 π t)

\frac{\partial}{\partial t} (9 π t) = 9 π

= e^{- 2 x} (- sin (9 π t) \cdot 9 π)

Simplify

= - 9 π e^{- 2 x} sin (9 π t)

\frac{1}{2} arctan (2 x)

n = 1 \sum \infty 3 e^{- 4 n}

f (x) = \frac{1}{x ^{2} + 4}, (1, \frac{1}{5})

\int 3 e^{x} - 3 x e^{x^{2}} d x

What is (\partial)/(\partial t)(e^{-2x}cos(9pit)) ?
The answer to (\partial)/(\partial t)(e^{-2x}cos(9pit)) is -9pie^{-2x}sin(9pit)