How do you differentiate #y=e^(-x/4)#?

1 Answer
Mar 4, 2018

#dy/dx=-e^(-x/4)/4#

Explanation:

In order to differentiate a function of a function, we use the chain rule. In other words, if #y=f(u)# and #u=f(x)#, then

#dy/dx=dy/(du)(du)/dx#

In this case, let #u=-x/4# and #y=e^u#. Then

#dy/(du)=e^u=e^(-x/4)#;

#(du)/dx=-1/4#

and, importantly,

#dy/dx=dy/(du)(du)/dx=e^(-x/4)(-1/4)=-e^(-x/4)/4#