Derivative function. Is the book wrong?

In summary, a derivative function is a mathematical tool used to measure the rate of change of a function at a specific point. It is calculated by taking the limit of the difference quotient as the change in input approaches zero. This can be done using various methods, such as the power rule, product rule, or quotient rule. A derivative function differs from a derivative, as the former is a general formula while the latter is a specific value at a given point. While a derivative function cannot be wrong, there may be errors in its calculation resulting in incorrect results. It is possible for a book to have incorrect information about derivative functions, so it is important to verify information from reliable sources.
  • #1
noahsdev
29
0
Differentiate the following with a positive index:
[itex]\frac{2}{\sqrt[3]{x}}[/itex]
What the book says:
[itex]\frac{-2}{3x^ \frac{2}{3}}[/itex]
But shouldn't it be:
[itex]\frac{-2}{3x^ \frac{4}{3}}[/itex]
I just wan't to know if I'm doing something wrong, thanks :).
 
Last edited:
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  • #3
Your book is wrong.
 
  • #4
Cool thanks, just wanted to check.
 
  • #5


I can confirm that the book is incorrect in this case. The correct derivative of 2x^(1/3) is -2/3x^(2/3), not -2/3x^(4/3). This can be verified by using the power rule for derivatives, which states that the derivative of x^n is nx^(n-1). In this case, n=1/3, so the derivative would be (1/3)x^(1/3-1) = (1/3)x^(-2/3) = -2/3x^(2/3). It is important to carefully follow the rules and guidelines for differentiation to avoid any errors in calculations.
 

1. What is a derivative function?

A derivative function is a mathematical tool used to measure the rate of change of a function at a specific point. It shows how the output of a function changes in response to small changes in the input.

2. How is a derivative function calculated?

The derivative function is calculated by taking the limit of the difference quotient as the change in the input approaches zero. This can be done using various methods, such as the power rule, product rule, or quotient rule.

3. What is the difference between a derivative function and a derivative?

A derivative function is the general formula for calculating the derivative of any function. A derivative, on the other hand, is the specific value of the derivative function at a particular point.

4. Can a derivative function be wrong?

No, a derivative function is a mathematical formula and cannot be wrong. However, there may be errors in the calculation of the derivative function, which can lead to incorrect results.

5. Is it possible for a book to have incorrect information about derivative functions?

Yes, it is possible for a book to have incorrect information about derivative functions. It is always important to double check and verify information from reliable sources.

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