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

We differentiate here to find the gradient, dy/dx, i.e. the differenitial of y in terms of x. As the right handside is purely dependant on x, this is simple. We can just multiply through by the power, i.e. 2x3=6, then negate the power by one, 3-1=2. Therefore giving us dy/dx = 6x^2.