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问题: 有关导数的题

函数f(x)在R上可导,函数F(x)=f(x^2-4)+f(4-x^2),求F'(2)
(答案为0)

解答:

函数f(x)在R上可导,函数F(x)=f(x^2-4)+f(4-x^2),

F'(x) =f'(x^2-4)(2x) + f'(4-x^2)(-2x)
=2x(f'(x^2-4)-f(4-x^2))

F'(2) = 2*2*(f'(0)-f'(0)) = 0.