How many degrees are there between the hour and minute hands when it’s 3:15 PM?

People have given me answers to this one ranging from 0^{\circ} to 75^{\circ} (and many answers in between). The big hand is on the three; the little hand is one-quarter of the way between the three and the four. The answer must be one-quarter of one-twelfth of 360^{\circ} . That is, one-quarter of 30^{\circ} . That is, 7.5^{\circ} (or \frac{\pi}{24} radians if you … Read more

Differentiate x^x with respect to x

    \[ \frac{dx^x}{dx} = \; ?\]

This problem is a popular interview question at places that require a quantitative mindset. Finding derivatives is a purely mechanical process which doesn’t require any creativity and once you’re used to parsing expressions and applying the rules, you can determine the derivative of any explicit expression you are given.

There are two ways … Read more