How to Correctly Apply the Quotient Rule in Differentiation?

Thread starter DollarBill
Start date Oct 6, 2008
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Differentiating quotient

In summary, the quotient rule for differentiation is a specific rule used to find the derivative of a fraction. It states that the derivative of a quotient is equal to the bottom function multiplied by the derivative of the top function, minus the top function multiplied by the derivative of the bottom function, all divided by the square of the bottom function. This rule is necessary for differentiating fractions, which cannot be done using the power rule or product rule. It should be used whenever a function can be written as a fraction, and it can be applied to any type of fraction with any combination of constants, variables, or other functions in the numerator and denominator. Common mistakes when using the quotient rule include forgetting to square the bottom function in the denominator and not applying

Oct 6, 2008

DollarBill

Homework Statement

X / 1+sinX

The Attempt at a Solution

Quotient rule

(1+sinX)(1)-X(1+cosX) / (1+sinX)²

To:

1+sinX-X-XcosX / (1+sinX)²

But when I look at the answer in the back of the book, it's wrong.

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Oct 6, 2008

gabbagabbahey

Homework Helper

Gold Member

Is the derivative of 1+sinX really 1+CosX? I thought the derivative of 1 was zero. ;0)

Oct 6, 2008

DollarBill

I always make these stupid mistakes

Thanks

Related to How to Correctly Apply the Quotient Rule in Differentiation?

1. What is the quotient rule for differentiation?

The quotient rule for differentiation states that when differentiating a quotient (a fraction), the derivative is equal to the bottom function multiplied by the derivative of the top function, minus the top function multiplied by the derivative of the bottom function, all divided by the square of the bottom function.

2. Why is the quotient rule necessary for differentiation?

The quotient rule is necessary for differentiation because it allows us to find the derivative of a fraction, which cannot be done using the power rule or product rule. It is a specific rule designed to handle the differentiation of a quotient, and without it, we would not be able to find the derivative of many functions that involve fractions.

3. How do I know when to use the quotient rule for differentiation?

The quotient rule should be used whenever you have a function that can be written as a fraction, with a top function and a bottom function. If you try to use the power rule or product rule on a fraction, you will get the wrong answer, so the quotient rule must be used instead.

4. Can I use the quotient rule for any type of fraction?

Yes, the quotient rule can be used for any type of fraction, including fractions with constants, variables, or other functions in the numerator and denominator. The rule remains the same regardless of the specific functions involved in the fraction.

5. Are there any common mistakes when using the quotient rule for differentiation?

One common mistake when using the quotient rule is forgetting to square the bottom function in the denominator. Another mistake is not applying the chain rule when the top or bottom function is a composite function. It is important to carefully follow the steps of the quotient rule and check your work to avoid these mistakes.