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,

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

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