F''(x) Second Derivative problem

In summary, the second derivative of the function f(x) = 3e^-x2 is 6x^2e^x2 - 6xe^x2. To find this, you first need to use the chain rule to find the first derivative, which is ?xe^(x^2). Then, use the product rule to find the second derivative, which is f'(x)g(x)+f(x)g'(x). Remember to use the chain rule again on the derivative of the second function.
  • #1
oowhitey
3
0

Homework Statement


find f''(x) <-- second derivative
f(x) = 3e^-x2 <-- that 2 is x squared

Homework Equations





The Attempt at a Solution


my attempt was 6x^2 e^x2
 
Physics news on Phys.org
  • #2
Try taking the first derivative first, then take the second derivative.
 
  • #3
oowhitey said:

Homework Statement


find f''(x) <-- second derivative
f(x) = 3e^-x2 <-- that 2 is x squared

The Attempt at a Solution


my attempt was 6x^2 e^x2


On the right track, but you're not quite remember your rules correctly.

For the first derivative, use the chain rule. Derivative of the outside 3e^(x^2) times the derivative of the inside (x^2)

Once you've got that, you're going to have a function that is an x times an exponential along the lines of ?xe^(x^2). From there, you need to use the product rule. Which is the derivative of the first function (?x) times the second function (e^(x^2)) plus the first function times the derivative of the second function. Or f'(x)g(x)+f(x)g'(x) (should be familiar from your text) On the derivative of your second function, don't forget the chain rule again!

Hopefully that helps, or if not, that someone can come and correct me.
 
  • #4
thanks that helped a bunch i think i got it.
 

What is the second derivative of a function?

The second derivative of a function, denoted as f''(x), is the derivative of the first derivative of the function. It represents the rate of change of the slope of the function at a particular point.

Why is the second derivative important?

The second derivative allows us to analyze the concavity of a function, which helps in identifying the maximum and minimum points of the function. It also helps in determining the nature of the graph, whether it is increasing or decreasing at a given point.

How do you find the second derivative of a function?

To find the second derivative of a function, you first need to find the first derivative of the function. Then, you apply the derivative rule again to the first derivative to get the second derivative. You can also use the quotient rule or the product rule to find the second derivative of more complex functions.

What does a positive or negative second derivative indicate?

A positive second derivative indicates that the function is concave up, meaning it is increasing at an increasing rate. A negative second derivative indicates that the function is concave down, meaning it is decreasing at an increasing rate.

How is the second derivative used to find inflection points?

An inflection point is a point where the concavity of the function changes. To find the inflection points, we set the second derivative equal to 0 and solve for x. The resulting values represent the x-coordinates of the inflection points on the graph of the function.

Similar threads

Replies
1
Views
471
  • Calculus and Beyond Homework Help
Replies
22
Views
2K
  • Calculus and Beyond Homework Help
Replies
4
Views
549
  • Calculus and Beyond Homework Help
Replies
5
Views
887
  • Calculus and Beyond Homework Help
Replies
6
Views
536
  • Calculus and Beyond Homework Help
Replies
23
Views
919
  • Calculus and Beyond Homework Help
Replies
8
Views
441
  • Calculus and Beyond Homework Help
Replies
9
Views
936
  • Calculus and Beyond Homework Help
Replies
2
Views
892
Replies
9
Views
696
Back
Top