Solve d2y/dx3: Step-by-Step Guide

  • Thread starter baba_944
  • Start date
  • Tags
    Derivative
These derivatives can be found by applying the power rule and chain rule, among other derivative rules. If you encounter any confusion or errors, it is recommended to consult a teacher or seek out an errata sheet for your textbook.
  • #1
baba_944
8
0

Homework Statement


[/B]
I've tried to search this up but to no avail. How am I suppose to solve this:

d2y/dx3

Homework Equations


N/A

The Attempt at a Solution



Here's what I think I need to do:

1: Square and cube y and x respectively.
2: Find the second and third derivative of y and x respectively.

Thank you.
 
Physics news on Phys.org
  • #2
This looks like a typo, I think you need to ask your teacher what they want here or of course you could compute the ##d^2y/dx^2## and the ##d^3y/dx^3##

The superscripts aren't powers and these aren't fractions of differentials.

The notation means:
- 2nd derivative of y with respect to x for ##d^2y/dx^2## and
- 3rd derivative of y with respect to x for ##d^3y/dx^3##

Check to see if your book has an errata sheet online which would indicate whether its a typo that is if this came from your book otherwise check with your teacher.
 
Last edited:
  • #3
Human error on my behalf. I mistype it. But yeah, thank you. I'm self-teaching (as scary enough as it is, ha ha) so no teacher besides myself

So basically it means to take the second (or nth) derivative? Thank you. .
 
  • #4
Yes
 

FAQ: Solve d2y/dx3: Step-by-Step Guide

1. What is the meaning of d2y/dx3?

The notation d2y/dx3 represents the third derivative of a function y with respect to x. This means that it is the rate of change of the rate of change of the rate of change of y with respect to x. It is also known as the third order derivative.

2. Why is it important to solve d2y/dx3?

Solving d2y/dx3 allows us to find the rate of change of the rate of change of a function at a specific point. This can be useful in many areas of science and mathematics, such as physics, engineering, and economics.

3. How do you solve d2y/dx3 step-by-step?

Step 1: Determine the function y and its derivatives up to the third order.

Step 2: Substitute the third derivative d2y/dx3 into the function.

Step 3: Use the appropriate differentiation rules to find the third derivative.

Step 4: Simplify the resulting expression as much as possible.

Step 5: Evaluate the third derivative at the given point or interval.

4. Can you provide an example of solving d2y/dx3?

Example: Given y = 3x^4 - 2x^3 + 5x^2, find d2y/dx3 at x = 2.

Solution: Step 1: y' = 12x^3 - 6x^2 + 10x

y'' = 36x^2 - 12x + 10

d2y/dx3 = 72x - 12

Step 2: Substitute x = 2 into the expression for d2y/dx3.

d2y/dx3 = 72(2) - 12 = 144 - 12 = 132

Therefore, d2y/dx3 at x = 2 is equal to 132.

5. What are the common applications of solving d2y/dx3?

One common application is in physics, where d2y/dx3 represents acceleration. By solving for d2y/dx3, we can determine the acceleration of an object at a specific point in time. It is also used in optimization problems, where the third derivative can help find the minimum or maximum value of a function.

Back
Top