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Question

Suppose f and g are functions having second derivatives f''  and g''  every where, if f(x).g(x)=1  for all x  and f'  and g'  are never zero, then f′′(x)f(x)g′′(x)g(x)  equals
 


Solution

The correct option is C
We havef(x)g(x)+g(x)f(x)=0g(x)g(x)+f(x)f(x)(1)Further f′′(x)g(x)+2f(x)g(x)+g′′(x)f(x)=0Divide throughout by f(x)g(x) and use (1)

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