第1199题：导数计算法则
对函数 f(x) f(x) f(x) 和 g(x) g(x) g(x) 且 g(x)≠0 g(x) \ne 0g(x)≠0 ，以下导数运算法则中，正确的是( ).
A. [f(x)g(x)]′\Big [ \dfrac{f(x)}{g(x)} \Big ]'[g(x)f(x)]′ =f′(x)g(x)+f(x)g′(x)[g(x)]2= \dfrac{f'(x) g(x) + f(x) g'(x)}{[g(x)]^2}=[g(x)]2f′(x)g(x)+f(x)g′(x)
B. [f(x)g(x)]′\Big [ \dfrac{f(x)}{g(x)} \Big ]'[g(x)f(x)]′ =f′(x)g(x)−f(x)g′(x)[g(x)]2= \dfrac{f'(x) g(x) - f(x) g'(x)}{[g(x)]^2}=[g(x)]2f′(x)g(x)−f(x)g′(x)
C. [f(x)g(x)]′\Big [ \dfrac{f(x)}{g(x)} \Big ]'[g(x)f(x)]′ =f′(x)g′(x)[g(x)]2= \dfrac{f'(x) g'(x) }{[g(x)]^2}=[g(x)]2f′(x)g′(x)
D. [f(x)g(x)]′\Big [ \dfrac{f(x)}{g(x)} \Big ]'[g(x)f(x)]′ =f′(x)g′(x)= \dfrac{f'(x)}{g'(x)}=g′(x)f′(x)
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