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

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Answer 1 · 2018-03-04T20:42:42

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

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#