What is the derivative of #e^(-x)#?

2 Answers
Aug 8, 2018

Answer:

#(dy)/(dx)=-e^(-x)#

Explanation:

Here ,

#y=e^-x#

Let,

#y=e^u and u=-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)#

Aug 8, 2018

Answer:

#-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)#