Question

How do you differentiate `f(x)=(1-e^x)^2` using the chain rule.?

Answer 1

I found: `f'(x)=-2e^x(1-e^x)`

Explanation:

You first derive the square as it is (red) and then multiply by the derivative of its argument (blue):
`f'(x)=color(red)(2)(1-e^x)^(color(red)(2-1))*color(blue)([0-e^x])=`
`=-2e^x(1-e^x)`