A) \[h'=(x).h''(x)\]
B) \[\frac{h(x)}{h''(x)}\]
C) \[\frac{h''(x)}{h(x)}\]
D) \[\frac{h(x)}{h'(x)}\]
Correct Answer: C
Solution :
Given, \[h(x)=f(x).g(x)\] and \[f'(x).g'(x)=c\] \[h''(x)=f''(x).g(x)+f'(x).g'(x)\] \[+f'(x).g'(x)+f(x).g''(x)\] \[h''(x)=f''(x).g(x)+f(x).g''(x)\] \[+2f'(x).g'(x)\] \[h''(x)=f''(x).g(x)+f(x).{{g}^{n}}(x)+2c\] ….(i) Now, we find \[\frac{f''(x)}{f(x)}+\frac{g''(x)}{g(x)}+\frac{2c}{f(x).g(x)}\] \[=\frac{f''(x).g(x)+g''(x).f(x)+2c}{f(x)\,.g(x)}\] \[=\frac{h''(x)}{h(x)}\] [from Eq. (i)]You need to login to perform this action.
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