Here we see the rate of change x '(t) of the function x(t) with respect to t represented by the magnitude of the vector drawn along the x-axis. To find the rate of change of f(x(t)) with respect to t, we use x '(t) as the horizontal component of the tangent vector to the parametrized curve at (x(t), f(x(t))), and our result is f '(x(t))x '(t).