• Ascendant78
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.
Ascendant78
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:

Put your two terms over a common denominator, expand the brackets and extract 4t^3 as a common factor in the numerator.

1 person
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!

No worries. Well done.

## 1. 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.

## 2. 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.

## 3. 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.

## 4. 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).

## 5. 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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