give an simple example of a function where you must use the quotient rule, product rule, and chain rule one time each to differentiate it. State the order of which rule is used first, second, and third. Your example must contain a trigonometric function within it. you do not need to differentiate your function.

Question

give an simple example of a function where you must use the quotient rule, product rule, and chain rule one time each to differentiate it. State the order of which rule is used first, second, and third. Your example must contain a trigonometric function within it. you do not need to differentiate your function.

Answer 1

Let's consider the function f(x) = (cos(x) + x^2) * e^(2x).

The order in which we will apply the rules is as follows:

1. Product Rule: We will differentiate the product of (cos(x) + x^2) and e^(2x) separately and then add them together.

2. Chain Rule: We will apply the chain rule when differentiating e^(2x) as it is composed of a function raised to a power.

3. Quotient Rule: After differentiating the product using the product and chain rule, we will apply the quotient rule to differentiate (cos(x) + x^2).

Please note that providing the actual differentiation is not required in this answer, but you can differentiate the function using the rules stated above to obtain the desired result.