help please?

Question

f(x)=(e^(-8x))(cos(3x))

derivative is?

Answer 1

f'(x) = (e^(-8x))(-3sin(3x)-8cos(3x))
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Ideas: When you have e^g(x) as a factor of f(x), it is still a factor after you take the derivative of f(x). Therefore, "copy" (e^(-8x)) first, and then find the other parts. In this way, you can get the answer in just one step.

Answer 2

Using a combination of chain and product rules,
f'(x) = - 3(e^(-8x))(sin(3x)) - 8(e^(-8x))(cos(3x))
f'(x) = - (e^(-8x))[3(sin(3x)) + 8(cos(3x))]

Answer 3

Use the product rule:
f' = (e^-8x)'cos(3x) + [cos 3x]' e^-8x
f' = (-8e^-8x)(cos 3x)+(-3sin3x)e^-8x
f' = (e^-8x)[-8cos3x - 3sin3x]