Is this a typo? Using Chain Rule and Product Rule

In summary, the conversation is about a possible typo in a given picture. The person asking the question usually does not like to second guess the text, but due to previous typos, they are unsure. The solution provided in the attempt includes a correction to the typo. The conversation ends with the acknowledgement that typos can be difficult to avoid in a large book of numbers.
  • #1
opus
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Homework Statement



This isn't really a homework problem, as the entire solution is laid out in the text. My question is in regards to a possible typo, which I have highlighted in blue in the given picture.
Usually I don't like to second guess the text, but this one has been absolutely plagued by typos and I usually have to go to the professor to see if it really is a typo or if I missed something.

Homework Equations

The Attempt at a Solution



My solution is ##h'(x) = (2x+1)^4(3x-2)^6(72x+1)##
 

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  • #2
Mine as well. The "7" and the "49" are wrong.
 
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  • #3
Ok thank you fresh. Really hate having to deal with typos, but I'm sure they're hard to avoid when writing an 800 page book of numbers.
 
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Related to Is this a typo? Using Chain Rule and Product Rule

1. What is the difference between the Chain Rule and the Product Rule?

The Chain Rule is used to find the derivative of a composite function, where one function is nested inside another. The Product Rule, on the other hand, is used to find the derivative of a product of two functions.

2. When should I use the Chain Rule and when should I use the Product Rule?

You should use the Chain Rule when you have a composite function, meaning one function is being applied to the output of another function. The Product Rule should be used when you have a product of two functions, meaning two functions are being multiplied together.

3. Can I use the Chain Rule and Product Rule together?

Yes, you can use both rules together when you have a function that is both a product and a composite. In this case, you would need to apply both rules in order to find the derivative.

4. Is there a specific order in which I should apply the Chain Rule and Product Rule?

Yes, there is a specific order. When using both rules together, you should apply the Chain Rule first and then the Product Rule. This is because the Chain Rule involves taking the derivative of the outer function first, while the Product Rule involves taking the derivatives of the two individual functions and then multiplying them together.

5. How do I know if I need to use the Chain Rule or Product Rule?

This will depend on the specific function you are trying to find the derivative of. If the function is a composite, you will need to use the Chain Rule. If the function is a product of two functions, you will need to use the Product Rule. It is important to recognize the structure of the function in order to determine which rule to use.

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