14-5 The Chain Rule.sagews

f(x) = sin(x)
g(x) = cos(x)
a = 1
frames = [plot(f(x + a*t)+ g(x - a*t), (x, -2*pi, 2*pi), ymin = -2, ymax = 2) for t in xsrange(-5, 5, 0.2)]
A = animate(frames)
show(A)

f(x) = sin(x) + (1/2)*sin(2*x)
g(x) = cos(x) + (1/3)*cos(3*x)
a = 1
frames = [plot(f(x + a*t)+ g(x - a*t), (x, -2*pi, 2*pi), ymin = -3, ymax = 3) for t in xsrange(-5, 5, 0.2)]
A = animate(frames)
show(A)

f(x) = 1/(x^2 + 1)
g(x) = x^2/(x^4 + 1)
a = 1
frames = [plot(f(x + a*t)+ g(x - a*t), (x, -10, 10), ymin = -1, ymax = 2) for t in xsrange(-5, 5, 0.2)]
A = animate(frames)
show(A)