More generally, if f(x₁,…,x_n) is a function of n variables x_i which each are functions of m variables t₁,…,t_m, then the multivariable version of the chain rule reads

The following rule that gives the derivative of the composition of two functions: If h(x) = (f∘g)(x) = f(g(x)) for all x, then h’(x) = f’(g(x))g’(x). For example, if h(x) = (x² + 1)³, then h = f ∘ g, where f(x) = x³ and g(x) = x² + 1. Then f’(x) = 3x² and g’(x) = 2x. So h’(x) = 3(x² + 1)² 2x = 6x(x² + 1)². Another notation can be used: if y = f(g(x)), write y = f(u), where u = g(x). Then the chain rule says that dy/dx = (dy/du)(du/dx). As an example of the use of this notation, suppose that y = (sin x)². Then y = u², where u = sin x. So dy/du = 2u and du/dx = cos x, and hence dy/dx = 2 sinx cosx.