- #1
Md. Abde Mannaf
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Member warned to not post homework questions in this forum section
How can it's solve using Leibniz Rule or other rule
- Thread starter Md. Abde Mannaf
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In summary, the conversation discusses using integration by parts and induction to solve a problem. The person initially struggles to solve it, but is given a useful link and suggestion to work out the case when ##m=1##. They are able to solve it and the concept is deemed useful.
- #2
fzero
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I would suggest using integration by parts and induction.
- #3
Md. Abde Mannaf
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i try. bt connot solve it. can you give me useful link or suggestionfzero said:
- #4
fzero
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Can you work out the case when ##m=1##?
- #5
Md. Abde Mannaf
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yes. when m=1 then value is = -1/(p+1)^2fzero said:
- #6
fzero
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Did you use the formula or integration by parts? Try the same kind of integration by parts when ##m=k+1##. You should be able to relate one of the terms to the integral for the case ##m=k##. This should suggest how to organize the proof by induction.
- #7
Md. Abde Mannaf
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your concept is very useful. thank you. i solve it. thank you very much again.fzero said:
1. What is Leibniz Rule and how is it used to solve problems?
Leibniz Rule, also known as the Product Rule, is a method used in calculus to find the derivative of a product of two functions. It states that the derivative of a product of two functions is equal to the first function multiplied by the derivative of the second function, plus the second function multiplied by the derivative of the first function.
2. When should I use Leibniz Rule to solve a problem?
Leibniz Rule is most commonly used when you need to find the derivative of a product of two functions. It is particularly useful when one or both of the functions cannot be easily differentiated using other rules, such as the Power Rule or Chain Rule.
3. What are the steps involved in using Leibniz Rule to solve a problem?
The steps for using Leibniz Rule are as follows: 1) Identify the two functions in the product, 2) Differentiate each function separately using the appropriate rules, 3) Multiply the first function by the derivative of the second function, 4) Multiply the second function by the derivative of the first function, and 5) Add the two results together to get the final answer.
4. Can Leibniz Rule be used to find higher order derivatives?
Yes, Leibniz Rule can be used to find higher order derivatives. To do this, you would simply apply the rule multiple times, using the previous result as one of the functions in the product.
5. Are there any other rules that can be used to find derivatives besides Leibniz Rule?
Yes, there are several other rules that can be used to find derivatives in calculus. Some of the most commonly used rules include the Power Rule, Chain Rule, and Quotient Rule. These rules can be used in combination with each other to solve more complex problems.
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