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

Banach