Series expansions and perturbation My professor said that $ f \left( y_1(x)+ \epsilon y_2(x)+... \right)= f(y_1(x)) +f'(y_1(x))\> (\epsilon y_2(x)+...) + ...$ but I have no idea how the series continues.  Has anyone seen this before?  Can you please tell me how the series progresses?

Taylor expansion:
$$+\frac{1}{2!}f''(y_1(x)) (\epsilon y_2(x)+\ldots)^2+\frac{1}{3!}f'''(y_1(x)) (\epsilon y_2(x)+\ldots)^3+\ldots$$
