d2y/dx2 = d/dy [1/2 (y'^2)] so how do we show that the LHS = RHS? starting from the LHS? i don't really understand. my lecturer made it become d2y/dx2 = dy/dx * d/dy * y' and he showed it equals RHS i understand how he get to dy/dx * d/dy * y' but shouldn't that become dy/dx *y' * d/dy which is (y')^2 * d/dy? so where did the 1/2 from the RHS come from? any help? thanks!