y=e^(–9x)cos(6x) find dy/dx.?

Question

e is raised to the -9x.

Answer 1

y = e^(-9x) cos(6x)

To solve this, we need to know the chain rule, the product rule, and these derivatives:
d/dx e^x = e^x
d/dx cos(x) = -sin(x)

dy/dx = e^(-9x) {-9} cos(6x) + e^(-9x) (-sin(6x)) (6)

Simplifying, we get

dy/dx = (-9)e^(-9x)cos(6x) - 6e^(-9x) sin(6x)