What is the derivative of e^{-2t}cos(x) ?

The derivative of e^{-2t}cos(x) is -e^{-2t}sin(x)

What is the first derivative of e^{-2t}cos(x) ?

The first derivative of e^{-2t}cos(x) is -e^{-2t}sin(x)

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\frac{d}{d x} (e^{- 2 t} cos (x))

- e^{- 2 t} sin (x)

Solution steps

\frac{d}{d x} (e^{- 2 t} cos (x))

Treat

t

as a constant

Take the constant out:

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

= e^{- 2 t} \frac{d}{d x} (cos (x))

Apply the common derivative:

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

= e^{- 2 t} (- sin (x))

Simplify

= - e^{- 2 t} sin (x)

What is the derivative of e^{-2t}cos(x) ?
The derivative of e^{-2t}cos(x) is -e^{-2t}sin(x)
What is the first derivative of e^{-2t}cos(x) ?
The first derivative of e^{-2t}cos(x) is -e^{-2t}sin(x)