Question

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

Answer 1

Answer:

$\frac{d}{dx} (e^{1-x}) = e^{1-x} (-1) = -e^{1-x}$

Step-by-step 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:

$\frac{df(u)}{dx} = \frac{df}{du} \frac{du}{dx}$

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:

$\frac{df(u)}{dx} = \frac{d}{du} (e^u) \frac{d}{dx} (1-x)$

$\frac{df(u)}{dx} = e^u (-1)$

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

$\frac{d}{dx} (e^{1-x}) = e^{1-x} (-1) = -e^{1-x}$