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Higher Derivatives  Definition
DEFINITION The second derivative of a real function f is the derivative of the derivative of f, and is denoted by f". The third derivative off is the derivative of the second derivative, and is denoted by f''', or f^{(3)}. In general, the nth derivative of f is denoted by f^{(n)}. If y depends on x, y = f (x), then the second differential of y is defined to be d^{2}y = f"(x)dx^{2}. In general the nth differential of y is defined by d^{n}y = f^{(n)}(x) dx^{n}. Here dx^{2} means (dx)^{2} and dx^{n} means (dx)^{n}. We thus have the alternative notations for the second and nth derivatives. The notation y" = f "M, y^{(n)} = f^{(n)}(x) is also used.


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