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Differential Calculus

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Joined:	9 Sep 2007
Post:	61

9 Sep 2007 21:50:23 IST

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on derivatives

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suppose f & g are functons having 2nd derivatives f" & g" everwhere . if f(x).g(x)=1 for all x & f' & g' r nevr 0, then f"(x)/f'(x)-g"(x)/g'(x) is what?

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Krishna Gopal Singh

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Joined: 29 Dec 2006

Posts: 5153

9 Sep 2007 23:42:02 IST

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g(x)=1/f(x)
so g'(x)=-f'(x)/(f(x))²
And g''(x)=((f(x))²*f''(x)-2f(x)*(f'(x))²)/(f(x))⁴

So g''(x)/g'(x)=f''(x)/f'(x)-2f'(x)/f(x)

Sof''(x)/f'(x)-g''(x)/g(x)=2f'(x)/f(x)=2f'(x)*g(x)

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