Derivative: y = 2 [e^(-x)] * x?

Question

Derivative: y = 2 [e^(-x)] * x

Short way; having a lot of trouble with this section.

If it's not too much trouble can you explain how to get the answer?

Answer 1

It's just the product rule (and a tiny bit of chain rule):

y = 2 [e^(-x)] * x
dy/dx = 2 [e^(-x)] d/dx {x} + 2 d/dx {e^(-x)} . x
= 2 e^(-x) . 1 + 2 (e^(-x) . d/dx {-x}) . x
= 2 e^(-x) + 2e^(-x) (-1) . x
= 2 e^(-x) (1 - x).

Answer 2

Hi Anon Yes Shy