**Unformatted text preview: **not inverted (see the discussion in part (a) above), so the wave moving to the left in Fig. (15.18) is ). ( x f-+ d) dx x d x d x df dx x df dx x df dx x df x f x f dx d dx dy ) ( ) ( ) ( ) ( ) ( ) ( )) ( ) ( (---+ =-+ =-+ = . x x dx df dx df-=-= At = x , the terms are the same and the derivatives is zero. (See Exercise 20-2 for a situation where the derivative of f is not finite, so the string is not always horizontal at the boundary.)...

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- Calculus, Derivative, dx dx dx