What is the d/(dt)(e^{-at}cos(xt)) ?

The d/(dt)(e^{-at}cos(xt)) is -ae^{-at}cos(tx)-e^{-at}xsin(tx)

What is the first d/(dt)(e^{-at}cos(xt)) ?

The first d/(dt)(e^{-at}cos(xt)) is -ae^{-at}cos(tx)-e^{-at}xsin(tx)

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\frac{d}{d t} (e^{- a t} cos (x t))

- a e^{- a t} cos (t x) - e^{- a t} x sin (t x)

Solution steps

\frac{d}{d t} (e^{- a t} cos (x t))

Treat

a, x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- a t}, g = cos (x t)

= \frac{d}{d t} (e^{- a t}) cos (x t) + \frac{d}{d t} (cos (x t)) e^{- a t}

\frac{d}{d t} (e^{- a t}) = - a e^{- a t}

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

= (- a e^{- a t}) cos (x t) + (- sin (x t) x) e^{- a t}

Simplify

= - a e^{- a t} cos (t x) - e^{- a t} x sin (t x)

y^{^{'}} = \frac{2 x ^{5} e ^{\frac{y}{x}} + x ^{3} y ^{2}}{x ^{4} y}

f (x) = - 2 x^{2} + 4 x - 4, at x = 3

\frac{\partial}{\partial x} (x + 3 y)

(lo g_{e} (x))^{^{'}}

(- 3, 5), (3, 5)

What is the d/(dt)(e^{-at}cos(xt)) ?
The d/(dt)(e^{-at}cos(xt)) is -ae^{-at}cos(tx)-e^{-at}xsin(tx)
What is the first d/(dt)(e^{-at}cos(xt)) ?
The first d/(dt)(e^{-at}cos(xt)) is -ae^{-at}cos(tx)-e^{-at}xsin(tx)