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Suppose f and g are functions having sec...

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'', g''` are never zero then `(f''(x))/(f'(x))-(g''(x))/(g'(x))` equals

A

`(-2f'(x))/(f(x))`

B

`(-2g'(x))/(g(x))`

C

`(-f'(x))/(f(x))`

D

`(2f'(x))/f(x)`

Text Solution

AI Generated Solution

To solve the problem, we need to find the expression \(\frac{f''(x)}{f'(x)} - \frac{g''(x)}{g'(x)}\) given that \(f(x)g(x) = 1\) for all \(x\). ### Step-by-step Solution: 1. **Start with the given equation:** \[ f(x)g(x) = 1 \] ...
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