What is the derivative of e^(-x)e−x?

2 Answers
maganbhai P.
Aug 8, 2018

(dy)/(dx)=-e^(-x)dydx=−e−x

Explanation:

Here ,

y=e^-xy=e−x

Let,

y=e^u and u=-xy=euandu=−x

:.(dy)/(du)=e^u and (du)/(dx)=-1

Using Chain Rule:

color(blue)((dy)/(dx)=(dy)/(du)*(du)/(dx)

:.(dy)/(dx)=e^u xx (-1)=-e^u

Subst, back u=-x

:.(dy)/(dx)=-e^(-x)

Jim G.
Aug 8, 2018

-e^(-x)

Explanation:

"differentiate using the "color(blue)"chain rule"

"given "y=f(g(x))" then"

dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"

d/dx(e^(-x))=e^(-x)xxd/dx(-x)=-e^(-x)

Related questions
See all questions in Chain Rule
Impact of this question
733700 views around the world
You can reuse this answer
Creative Commons License