A curve has the equation y = (x^2 - 5)e^(x^2). Find the x-coordinates of the stationary points of the curve.

This requires the chain rule and the product rule to be used to differentiate the function. The substitution u = x² can be used to make this easier. Using this, du/dx = 2x and y = (u-5)e^u. Using the product rule, dy/dx = e^u + (u-5)e^u = e^u(u-4). Substituting u = x² back in, dy/du = (x²-4)e^{x^2}. Now the chain rule can be used to find dy/dx: dy/dx = (dy/du)(du/dx) = 2x(x²-4)e^{x^2}. The stationary points are when dy/dy = 0. e^{x^2} is always > 0, so either 2x = 0 (x=0) or x²-4 = 0, giving x = -2 and x = 2, so the stationary points are at x = -2, 0 and 2.