How do you find the derivative of y=e^(-2x-1) * ln(-2x-1)?

1 Answer
Jun 21, 2018

-e^(-2x-1)/(-2x-1)-2ln(-2x-1)e^(-2x-1)

Explanation:

d/dxln(-2x-1)e^(-2x-1)
=d/dx[ln(-2x-1)]*e^(-2x-1)+ln(-2x-1)*d/dx(e^[-2x-1])
=1/(-2x-1)*d/dx(-2x-1)*e^[-2x-1]+e^[-2x-1]*d/dx[-2x-1]*ln(-2x-1)
={(-2*d/x[x]+d/dx[-1])e^[-2x-1]}/[-2x-1]+(-2*d/x[x]+d/dx[-1])ln(-2x-1)e^(-2x-1)
=[(0-2*1)e^(-2x-1)]/[-2x-1]+(0-2*1)ln(-2x-1)e^(-2x-1)
=-e^(-2x-1)/(-2x-1)-2ln(-2x-1)e^(-2x-1)