# Homework Help: How to find the derivative of y= x^-1/e^-x

1. Jan 31, 2009

### intenzxboi

1. The problem statement, all variables and given/known data
y = ((x)^−1) (e^−x)

3. The attempt at a solution

Solving this out i got
[(x^-1) - (x^-2)] e^-x

however the book is telling me the answer is
−(x^−1 + x^−2)e^−x

wouldnt that give me (-x^−1 - x^−2)e^−x ??
what did i do wrong??

2. Jan 31, 2009

### Staff: Mentor

Re: Differentiate

Apparently you lost a sign somewhere. I'm guessing that you forgot the factor of (-1) when you differentiated e^(-x).
$$d/dx(x^{-1}e^{-x}) = x^{-1} e^{-x} (-1) - x^{-2}e^{-x}$$
$$= -x^{-1}e^{-x} - x^{-2} e^{-x}$$
which agrees with the book's answer.

BTW, you're not "solving this out;" you're differentiating this function or calculating the derivative of the given function.

3. Jan 31, 2009

### intenzxboi

Re: Differentiate

Thanks i thought the derivative of e^-x stayed the same

4. Jan 31, 2009

### Hootenanny

Staff Emeritus
Re: Differentiate

$$\frac{d}{dx}e^x = e^x$$

However, in general (using the chain rule)

$$\frac{d}{dx} e^{f\left(x\right)} = f^\prime\left(x\right)e^{f\left(x\right)}$$

$$f\left(x\right) = -x$$

So

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

Do you follow?