# Arithmetic Question for Finding Derivative using Quotient Rule

• Joe_K
In summary, the conversation discusses finding the derivative of a given function using the quotient rule. The attempt at a solution involves expanding the numerator and simplifying it to the desired answer. The conversation also mentions the use of basic arithmetic and collecting like terms in order to simplify the expression.
Joe_K

## Homework Statement

Find dy/dx for the following function:

y = (11-cos(x))/(2+cos(x))

## Homework Equations

Quotient Rule:

y'= ((g(x))(f'(x)) - (f(x))(g'(x)))/ (g(x)^2)

## The Attempt at a Solution

I used the quotient rule to come up with this:

y'= ((2+cos(x))(sin(x)) - (11-cos(x))(-sin(x))) / ((2+cos(x))^2)

Now, the trouble that I am having is simplifying this.

The final answer should turn out to be :

(13sin(x))/(cos(x)+2)^2

I am overlooking some basic arithmetic here, but I can't seem to find out what I am missing. Am I supposed to multiply out the expressions first and then combine like terms? Basically, how do I go from the expanded version to the simplified version? Thank you

Yes try expanding it; simplifying it to the required expression is just a matter of collecting like terms

Your denominator looks to be in the same form as the desired answer.

Play around with the numerator.

## 1. What is the Quotient Rule in calculus?

The Quotient Rule is a formula used in calculus to find the derivative of a function that is a quotient of two other functions. It states that the derivative of f(x)/g(x) is equal to (g(x)*f'(x) - f(x)*g'(x)) / (g(x))^2.

## 2. How is the Quotient Rule used to find the derivative of a function?

The Quotient Rule is used by taking the derivative of the numerator and denominator separately, and then plugging those values into the formula (g(x)*f'(x) - f(x)*g'(x)) / (g(x))^2 to solve for the derivative.

## 3. When should the Quotient Rule be used instead of other derivative rules?

The Quotient Rule should be used when the function is a quotient of two other functions, and when it is not possible to simplify the function using other derivative rules such as the Power Rule or Product Rule.

## 4. Are there any restrictions when using the Quotient Rule?

Yes, the Quotient Rule cannot be used if the denominator of the function is equal to 0. In this case, the function is undefined and the Quotient Rule does not apply.

## 5. Can the Quotient Rule be used for functions with multiple variables?

Yes, the Quotient Rule can be used for functions with multiple variables, as long as the variables are independent of each other. The derivative will be taken with respect to one variable at a time, while treating the rest as constants.

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