derivative for finite positive integral K

Question

I can't figure out what this question is asking for,

Compute the derivative with respect to x of the function

$$ f(x) = \log\left(\sum_{k = 1}^K \exp(k x^k)\right)\:\text{ for finite, positive, integral }K. $$

I am assuming that I need to take the derivative of this function where:

$$ \frac{df(u)}{dx} = \frac{df}{du}\frac{du}{dx} $$ where $u=\sum_{k = 1}^K \exp(k x^k) f = log(u)$

And yes, it is an assignment question, in my Machine Learning class.

Answer 1

With your definition of $u$, what you are asked to find is $$ \frac{df}{dx}=\frac{d}{dx}\log u=\frac{d\log u}{du}\,\frac{du}{dx}=\frac{1}{u}\,\,u'. $$ I'm sure you can find $u'$.