Simple Derivation giving me a headache.

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In summary, Simple Derivation is a process that involves finding the derivative of a function using basic rules and formulas. It can be a challenging concept to grasp, causing headaches for many students. However, with practice and understanding of the fundamental principles, it can become a useful tool in solving more complex mathematical problems.
  • #1
Jimbo57
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Homework Statement


Deriving http://www4d.wolframalpha.com/Calculate/MSP/MSP20181a00e6i82g005gag00005gb4c7hic8g2i3hi?MSPStoreType=image/gif&s=57&w=79&h=43


Homework Equations





The Attempt at a Solution



My attempt gives me:
-48/(x^2-16)^2 + 192x^2/(x^2-16)^3 via product rule

Wolfram alpha gives me this for an answer

http://www4d.wolframalpha.com/Calculate/MSP/MSP40371a00e53i06h6352d000061574g9ehi6a9958?MSPStoreType=image/gif&s=15&w=224&h=48

I can't seem to figure out how to match my answer with Wolfram, even though it's not a tough derivative. Am I maybe not simplifying enough?
 
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  • #2
Jimbo57 said:

Homework Statement


Deriving http://www4d.wolframalpha.com/Calculate/MSP/MSP20181a00e6i82g005gag00005gb4c7hic8g2i3hi?MSPStoreType=image/gif&s=57&w=79&h=43

Homework Equations


The Attempt at a Solution



My attempt gives me:
-48/(x^2-16)^2 + 192x^2/(x^2-16)^3 via product rule

Wolfram alpha gives me this for an answer

http://www4d.wolframalpha.com/Calculate/MSP/MSP40371a00e53i06h6352d000061574g9ehi6a9958?MSPStoreType=image/gif&s=15&w=224&h=48

I can't seem to figure out how to match my answer with Wolfram, even though it's not a tough derivative. Am I maybe not simplifying enough?

A simple trick that you can use to see if your answer actually matches up is to let x be a transcendental number like [itex]\pi[/itex] in your answer, then in Wolfram's. Since we're dealing with rational coefficients and exponents throughout, there is no way they can match up unless the answers are algebraically equivalent. They do match up in this case.

So it's just a matter of rearranging your equation. Try reexpressing -48/(x^2-16)^2 as [itex]-\frac{48(x^2 - 16)}{{(x^2 - 16)}^3}[/itex] for starters, then combine the numerators over a common denominator.
 
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  • #3
The answers are equivalent. In order to get it into the same form, you need to make a common denominator.
 
  • #4
Ahh I see it now, thanks so much guys. Simple mistake, maybe I need a break...
 

FAQ: Simple Derivation giving me a headache.

1. What is a simple derivation?

A simple derivation is a mathematical process that involves using known formulas and principles to arrive at a new formula or equation. It is often used to solve complex problems by breaking them down into smaller, more manageable steps.

2. Why does simple derivation give me a headache?

Simple derivation can be challenging because it requires a strong understanding of mathematical principles and the ability to manipulate equations and formulas. It can also involve multiple steps, which can be mentally taxing and lead to headaches.

3. How can I make simple derivation easier?

One way to make simple derivation easier is to practice regularly and familiarize yourself with common formulas and principles. It can also be helpful to break down complex problems into smaller, more manageable steps. Additionally, seeking help from a tutor or classmate can provide valuable insights and make the process less overwhelming.

4. Are there any tools or resources that can assist with simple derivation?

Yes, there are many online tools and resources available that can assist with simple derivation. These may include equation solvers, step-by-step guides, and video tutorials. It may also be helpful to consult textbooks or other reference materials for additional guidance.

5. How can I check if my simple derivation is correct?

To check if your simple derivation is correct, you can use the resulting formula or equation to solve a sample problem or plug in different values to see if it produces the expected result. You can also verify your work by comparing it to solutions from reputable sources or seeking feedback from a teacher or tutor.

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