Question about reducing an answer from a derivative?

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In summary, the person is struggling with finding the simplified answer to a derivative and needs to understand the process for using it in solving equations for magnitudes. They mention it being a difficult task and provide an example of the derivative. After some guidance, they are able to understand and thank the other person for their help.
  • #1
Ascendant78
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Ok, I can get to the answer in yellow, but I am not sure how they went from the answer in yellow to the simplified one in white. I really need to know how to do this because we are using these derivatives for magnitudes (solving for principal normal unit vectors), where I have to square them and take square roots. So, I'm sure you could imagine having to square equations like this, factor out, try to take roots, etc., is a complete and utter nightmare. Each problem is taking me about 30-40mins, and there are 9 homework problems.

Anyway, here is the derivative:

a_Screen_Shot.jpg


b_Screen_Shot.jpg
 
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  • #2
Put your two terms over a common denominator, expand the brackets and extract 4t^3 as a common factor in the numerator.
 
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  • #3
Simon Bridge said:
Put your two terms over a common denominator, expand the brackets and extract 4t^3 as a common factor in the numerator.

Ah, ok I see it now. Thanks again!
 
  • #4
No worries. Well done.
 

FAQ: Question about reducing an answer from a derivative?

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It measures how much a function is changing as its input variable changes.

Why is it important to reduce an answer from a derivative?

Reducing an answer from a derivative allows us to simplify complex equations and better understand the behavior of a function. It also helps us find critical points and slopes of a function, which are important in many applications.

How do you reduce an answer from a derivative?

To reduce an answer from a derivative, we use algebraic techniques and mathematical rules to simplify the expression. This can include factoring, canceling out common terms, and using derivative rules such as the power rule or chain rule.

Can you give an example of reducing an answer from a derivative?

Sure! Let's say we have the function f(x) = 3x^2 + 2x + 1. The derivative of this function is f'(x) = 6x + 2. To reduce this answer, we can factor out the common factor of 2 to get f'(x) = 2(3x + 1).

What are the benefits of reducing an answer from a derivative?

Reducing an answer from a derivative can help us find the maximum and minimum values of a function, determine the slope of a curve, and understand the behavior of a function. It also allows us to simplify complex equations and make them more manageable for further calculations.

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