The gradient is the derivative, or differential, of the function y=x^2-3. the derivative of x^n is nx^(n-1) and the derivative of a constant is zero so y'=dy/dx=gradient=2x, which means that the gradient is dependent on x, on where you are on the curve y=x^2-3. The gradient can also be found by taking a point a very small distance away from x, call it dx. The new value of y will change by a small value dy, so y+dy=(x+dx)^2-3=x^2+2xdx+dx^2-3. So subtracting y=x^2-3 from this we get: dy=2xdx+dx^2; and dividing through by dx we get: dy/dx=2x+dx. But dx on the right-hand side is very small, much smaller than 2x, so we can ignore it as it gets close to zero. dy/dx is the slope or gradient at the point (x,y), and 2x is the same value we get when we use calculus.