# Thread: How can I derivate this?

1. ## How can I derivate this?

$e^{-x}}\sum _{k=0}^{2011}{\frac {{x}^{k}}{k!}$
Thank you!

2. ## Re: How can I derivate this?

Use the product rule and:
$\frac{d}{dx}\left(\sum_{k=0}^{2011} \frac{x^k}{k!}\right)=\sum_{k=0}^{2011} \frac{d}{dx}\left(\frac{x^k}{k!}\right)$

3. ## Re: How can I derivate this?

OKay, but i dont know how to derivate that factorial stuff

4. ## Re: How can I derivate this?

You are only taking the derivative with respect to x, k! is constant.

5. ## Re: How can I derivate this?

Then it is only kx^k-1 /k!?

6. ## Re: How can I derivate this?

Originally Posted by gotmejerry
Then it is only kx^k-1 /k!?
$\frac{kx^{k-1}}{k!}$ is correct, however, you can use your definition of a factorial to cancel a factor of k giving $\dfrac{x^{k-1}}{(k-1)!}$

But don't forget your other term and use the product rule

Thank you!