# Calculate the derivative of: 8³√x

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In summary, the conversation discusses how to calculate the derivative of 8³√x and similar problems. The answer is given as 8/3³√x¹¹, and the power rule is mentioned as the correct method for solving the problem. The conversation also includes a clarification on the notation used and a thank you message for the help provided.
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I'm not sure how to calculate the derivative of: 8³√x :if anyone can help me or show me how to calculate the derivatives of similar problems such as this it would be greatly appreciated. Thanks

It says in the back of the book that the answer is: 8/3³√x¹¹

I have never done one of these problems before and this is how i tried to approach it:
8³√x
dy/dx = 8 X 1/2 ^3 x^1/2 - 1
= 8/2^3 x^-1/2

Thats what i kinda thought at first but it is so wrong

I've looked through the worked examples in the book and there are no problems like this. This is the only problem out of this section of exercises that I am having trouble with...its really disapointing because it broke me groove and its really annoying me that I can't work it out!

Is that 8^3 * sqrt(x), or 8 times the cubed root of x?

pete5383 said:
Is that 8^3 * sqrt(x), or 8 times the cubed root of x?

i think its 8 times the cubed root of x

Write it as 8.x^(1/3) and differentiate normally.

cool thanks a lot :D

## 1. What is the power rule for calculating derivatives?

The power rule states that the derivative of x^n is n*x^(n-1), where n is any real number.

## 2. How do you calculate the derivative of a radical function?

To calculate the derivative of a radical function, you can use the power rule and rewrite the function in exponent form. For example, the function 8³√x can be rewritten as x^(1/3). The derivative would then be (1/3)*x^(-2/3).

## 3. Can the power rule be applied to fractional exponents?

Yes, the power rule can be applied to fractional exponents. The only difference is that the exponent will become a negative number when you subtract 1 from it.

## 4. Are there any other rules for calculating derivatives?

There are several other rules for calculating derivatives, such as the product rule, quotient rule, and chain rule. These rules are used for more complex functions that cannot be simplified using the power rule.

## 5. How can I check if my derivative calculation is correct?

You can check your derivative calculation by plugging in values for x and comparing the result to the original function. If they match, then your calculation is likely correct. You can also use online derivative calculators or consult with another mathematician or scientist for validation.

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