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Let f(x) and g(x) be real valued functio...

Let f(x) and g(x) be real valued functions such that f(x)g(x)=1, `AA x in R."If "f''(x) and g''(x)" exists"AA x in R and f'(x) and g'(x)`
are never zero, then prove that `(f''(x))/(f'(x))-(g''(x))/(g'(x))=(2f'(x))/(f(x))`

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AI Generated Solution

To prove the equation \[ \frac{f''(x)}{f'(x)} - \frac{g''(x)}{g'(x)} = \frac{2f'(x)}{f(x)}, \] given that \( f(x)g(x) = 1 \) for all \( x \in \mathbb{R} \), we will follow these steps: ...
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