Solve d2y/dx3: Step-by-Step Guide

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    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
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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.
 
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  • #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.
 
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  • #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
 

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.

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