1) First note that the function is continuous at , so a derivative could exist. To find the derivative for every point except , just use the product and chain rule and note that
To see if the derivative exists at just find the left and right limit of at . The term is clearly 0 for both of these limits, but the term flucuates between 1 and -1, so the limits do not exist and thus the derivitve does not exist at .
I am still working on the second part but I am 100% sure you have typed the question incorrectly (a simple graph will show you it is always increasing). So you probably need to show f is not DECREASING, in which case you show the derivative is always positive.