(Q12.) So, you think you can take the derivative? | Summary and Q&A

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April 13, 2014
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blackpenredpen
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(Q12.) So, you think you can take the derivative?

TL;DR

An explanation of how to use the quotient rule to find the derivative of a function involving exponential terms.

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Questions & Answers

Q: How can we modify a function with a negative exponent to be compatible with the answer choices?

By moving the negative exponent to the denominator and multiplying the top and bottom by the denominator, the function can be rewritten in a compatible format.

Q: What is the purpose of multiplying the top and bottom by the denominator?

Multiplying the top and bottom by the denominator ensures that the smaller fraction in the denominator cancels out, simplifying the function.

Q: What is the quotient rule?

The quotient rule is a method used to find the derivative of a function that is a quotient of two functions. It involves multiplying the bottom function by the derivative of the top function, and subtracting the top function multiplied by the derivative of the bottom function.

Q: How does the quotient rule help in finding the derivative of the function?

By applying the quotient rule to the function, we can find the derivative step-by-step, simplifying and rearranging terms along the way.

Summary & Key Takeaways

  • The video explains the steps to rewrite a function with a negative exponent to make it compatible with the answer choices.

  • The original equation is modified by moving the negative exponent to the denominator and multiplying the top and bottom by the denominator.

  • The quotient rule is applied to find the derivative of the function, which involves multiplying and subtracting certain terms.

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