Struggling with the 2nd Derivative of f(x)=x/x^2+1?

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In summary, the second derivative is a mathematical concept that describes the rate of change of the rate of change of a function. It can be calculated by taking the derivative of the first derivative using various rules. "2nd derivative trouble" refers to when the second derivative of a function is undefined or does not exist at a certain point. The second derivative is important for determining concavity, finding points of inflection, and identifying maximum and minimum values of a function. To overcome "2nd derivative trouble", alternative calculation methods and other techniques may be necessary.
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ande1717
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f(x)=x/x^2+1
f'(x)= 1-x^2/(x^2+1)^2
But then I can't seem to work through taking the 2nd derivative, perhaps I am not using the chain rule right.
I get -4x^5-2x^3-2x/(x^2+1)^4
But that's not right... please help!
 
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You double-posted, probably by accident. But let's stay in one thread.
 

FAQ: Struggling with the 2nd Derivative of f(x)=x/x^2+1?

What is the second derivative?

The second derivative is a mathematical concept used to describe the rate of change of the rate of change of a function. It is the derivative of the first derivative of a function.

How do you calculate the second derivative?

The second derivative can be calculated by taking the derivative of the first derivative. This can be done using the power rule, product rule, quotient rule, or chain rule depending on the complexity of the function.

What does it mean when a function has "2nd derivative trouble"?

When a function has "2nd derivative trouble", it means that the second derivative of the function does not exist or is undefined at a certain point. This is typically caused by a sharp change in the slope of the function or a point where the function is not differentiable.

Why is the second derivative important?

The second derivative is important because it can help determine the concavity of a function and identify points of inflection. It can also be used to find the maximum and minimum values of a function.

How can I overcome "2nd derivative trouble" in my calculations?

To overcome "2nd derivative trouble", you may need to use a different method to calculate the derivative, such as the limit definition of the derivative. You may also need to consider the behavior of the function at the point where the second derivative is undefined and use other techniques, such as the first derivative test, to analyze the function.

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