1. $y = \frac{1}{x}$ The derivative of $y = \frac{1}{x}$ can be computed in the following way. First, I highly recommend you to watch this clip , where 3blue1brown visualizes this function. The key part of the proof is that Since A and B are both on the curve of $y = \frac{1}{x}$, the x coordinate times the y coordinate is 1. That is to say: $A_x \cdot A_y = 1$ and $B_x \cdot B_y = 1$....