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In Problems 123, find the second derivative. 24 Find the third derivative of y = x^{2}  2/x. 25 A particle moves according to the equation s = 1  1/t^{2}, 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 d^{2}u/dx^{2} exists. If y = 3u, find d^{2}y/dx^{2}. 28 If d^{2}u/dx^{2} and d^{2}v/dx^{2} exist and y = u + v, find d^{2}y/dx^{2}. 29 If d^{2}u/dx^{2} exists and y = u ^{2}, find d^{2}y/dx^{2}. 30 If d^{2}u/dx^{2} and d^{2}v/dx^{2} exist and y = uv, find d^{2}y/dx^{2}. 31 Let y = ax^{2} + bx + c be a polynomial of degree two. Show that dy/dx is a linear function and d^{2}y/dx^{2} 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.)


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