How do I find second derivatives

Thread starter afcwestwarrior
Start date Oct 4, 2008
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Derivatives

In summary, a second derivative is a mathematical concept that represents the rate of change of the slope of a function. It is important in understanding the shape and behavior of a function, and can help find maximum and minimum points and points of inflection. To find the second derivative, one must first find the first derivative and then apply the same rules again. The notation for a second derivative is f''(x) or d^2y/dx^2, and it can be found for any differentiable function.

Oct 4, 2008

afcwestwarrior

Homework Statement

y=e^rx Y'=r*e^rx Y''=?

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Oct 4, 2008

Redbelly98

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Solve this problem instead:

y = r*e^rx
y' = ?

If you solve this problem then you've solved your problem.

Oct 5, 2008

HallsofIvy

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You find a second derivative by differentiating again. That is Redbelly98's point.

1. What is a second derivative?

A second derivative is a mathematical concept that represents the rate of change of the slope of a function. It is the derivative of the derivative of the original function.

2. Why is finding second derivatives important?

Finding second derivatives can help us understand the shape and behavior of a function. It can also help us find maximum and minimum points, as well as points of inflection.

3. How do I find the second derivative of a function?

To find the second derivative of a function, you first need to find the first derivative and then take the derivative of that result. You can use the power rule, product rule, quotient rule, or chain rule to find the first derivative, and then apply the same rule again to find the second derivative.

4. What is the notation for a second derivative?

The notation for a second derivative is f''(x) or d²y/dx². The double prime symbol indicates that it is the second derivative.

5. Can I find the second derivative of any function?

Yes, you can find the second derivative of any function as long as it is differentiable. This means that the function must be continuous and have a well-defined slope at every point.