Question

If y=e^-x * cos(2x), then dy/dx is what?

Answer 1

use product rule
\[(fg)' = f'g + fg'\]
\[f' = -e^{-x}\]
\[g = -2 \sin(2x)\]

Answer 2

Use the product rule
(uv)' = u'v + v'u
\[u= e^{-x} \\
v =\cos(2x)

\]

Answer 3

\[
y=e^{-x} \cos(2x)\\
y'=- e^{-x} \cos(2x) -2 e^{-x} \sin(2x)

\]