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Calculus/second derivative

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Expert: - 4/25/2008


Question
i already found f'(x) but now i need to find f"(x). So I need the derivative of -1/x^2(x^2+1)^1/2.

Thanks

Answer
If the function given is 1/(x^2(x^2+1)^0.5), look at it as
1/(f(x)g(x)) where f(x)=x^2 and g(x)=(x^2+1)^0.5.  
Let h(x)=f(x)g(x), so what you're looking for is the
derivative of 1/h(x).

The derivative of one over some function is one over the
same function squared times the derivatve of that function.  
We can write that as h'(x)/h^2(x).  Looking back at the
problem, h(x) squared is f(x) squared times g(x) squared.

Here, the derivative of h(x) is found by the product rule.  
You know, f'g + fg'.  The derivative of f(x) is straight
forward, but the derivative of g(x) uses the chain rule.

Hopefully you have it down after reading (and maybe reading
it again).  When you have more questions about this problem
or any other problem, I will gladly help you more.

Have a great day.

Calculus

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