Question

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

Answer 1

`(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)`

Answer 2

`-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)`