How would you derive y = function of x; for example: y = 3x^3 + x^2 + x

The best way to remember derivatives is to use algebra, and the general function is y = axⁿ -> dy/dx = anx^n-1

So for this equation dy/dx = (3x3)x^3-1 + (2x1)x^2-1 + 1x^1-1

So the answer would be dy/dx = 9x² + 2x + 1

The last one may be confusing but as the power is 0, you remove the x and it becomes a whole number, in this case 1.