Derivative, Is my answer correct?

neutron star · 2009-10-25T22:45:03+00:00

Homework Statement y=sin^6(4Θ) Homework Equations The Attempt at a Solution dy/d\theta=24sin^5(4\theta)cos(4\theta)

Thread starter neutron star
Start date Oct 25, 2009
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Derivative

In summary, a derivative is a mathematical concept used in calculus to determine the rate of change of one variable with respect to another. To find the derivative of a function, you can use rules of differentiation such as the power, product, quotient, and chain rules. The derivative represents the slope of a curve or the instantaneous rate of change of a function. To check if your answer for a derivative is correct, you can take the derivative again or use online calculators or graphing tools. Common mistakes when finding derivatives include forgetting to use the chain rule, misapplying the product or quotient rule, and incorrectly simplifying the final answer. It is important to carefully follow the rules of differentiation and double-check your work to avoid these mistakes.

Oct 25, 2009

neutron star

Homework Statement

[tex]y=sin^6[/tex](4Θ)

Homework Equations

The Attempt at a Solution

[tex]dy/d\theta=24sin^5(4\theta)cos(4\theta)[/tex]

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Oct 25, 2009

Mark44

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neutron star said:

Homework Statement

[tex]y=sin^6[/tex](4Θ)

Homework Equations

The Attempt at a Solution

[tex]dy/d\theta=24sin^5(4\theta)cos(4\theta)[/tex]

Yes.

1. What is a derivative?

A derivative is a mathematical concept that represents the rate of change of one variable with respect to another. It is often used in calculus to determine the slope of a curve at a specific point.

2. How do you find the derivative of a function?

To find the derivative of a function, you can use the rules of differentiation, such as the power rule, product rule, quotient rule, and chain rule. These rules involve taking the derivative of each term in the function and combining them to find the overall derivative.

3. What does the derivative represent?

The derivative represents the slope of a curve at a specific point, or the instantaneous rate of change of a function.

4. How do I know if my answer for a derivative is correct?

You can check if your answer for a derivative is correct by taking the derivative again and seeing if it matches the original function. You can also use online calculators or graphing tools to visualize the derivative and compare it to your answer.

5. Are there any common mistakes when finding derivatives?

Yes, some common mistakes when finding derivatives include forgetting to use the chain rule, misapplying the product or quotient rule, and incorrectly simplifying the final answer. It is important to carefully follow the rules of differentiation and double-check your work to avoid these mistakes.