Hi! Let f: M \rightarrow N a local diffeomorphism, X a vectorfield on N. We define (f^{*} X)(x):= T_x f \cdot X(x), where T_x f is the tangential map assoiciated with f. I want to show that f^{*} [X,Y]=[f^{*}X, f^{*}Y], where [.,.] is the liebracket (Y another vector field). Can anybody help me please?

Banach