Problems

In Problems 1-23, find the second derivative.

24            Find the third derivative of y = x² - 2/x.

25            A particle moves according to the equation s = 1 - 1/t², t > 0. Find its acceleration.

26            An object moves in such a way that when it has moved a distance 5 its velocity is v = √s. Find its acceleration. (Use Example 3.)

27            Suppose u depends on x and d²u/dx² exists. If y = 3u, find d²y/dx².

28            If d²u/dx² and d²v/dx² exist and y = u + v, find d²y/dx².

29            If d²u/dx² exists and y = u ², find d²y/dx².

30            If d²u/dx² and d²v/dx² exist and y = uv, find d²y/dx².

31             Let y = ax² + bx + c be a polynomial of degree two. Show that dy/dx is a linear function and d²y/dx² is a constant function.

32            Prove that the nth derivative of a polynomial of degree n is constant. (Use the fact that the derivative of a polynomial of degree k is a polynomial of degree k - 1.)