Question

Differentiating Exponential functions In Exercise,find the derivative of the function. See Example 2 and 3.

y = e1 - x

Answer 1

`(d)/(dx) (e^(1-x)) = e^(1-x) (-1) = -e^(1-x)`

Explanation:

Assuming the following function
`y = e^(1-x)}` we want to find the derivate of this function.

For this case we need to apply the chain rule given by the following formula:

`(df(u))/(dx) = (df)/(du) (du)/(dx)`

On this case our function is
`f = e^u` and our value for u is
`u =1-x`

If we appply this rule we got this:

`(df(u))/(dx) = (d)/(du) (e^u) (d)/(dx) (1-x)`

`(df(u))/(dx) = e^u (-1)`

And now w can substitute
`u = 1-x` and we got:

`(d)/(dx) (e^(1-x)) = e^(1-x) (-1) = -e^(1-x)`