A curve has the equation y=x^3+2x+15. Find dy/dx.

Here, we are asked to differentiate with respect to x. That is what dy/dx stands for. So, we are only concerned with the terms involving x; that is x^3 and 2x. To differentiate you need to time x (and its coefficient) by its power and then subtract 1 from the power. For example, x^3 becomes 3x^2 and 2x becomes 2x^0, which is just 2.  So dy/dx=3x^2+2.