# 2.2.211 AP Calculus Exam practice problem

• MHB
• karush
In summary, the conversation is discussing a problem where $y$ is equal to $x \sin x$ and the question is asking for the derivative $\dfrac{dy}{dx}$, with multiple choice options provided. There is also a question about whether the notation $y'$ should be used in addition to $\dfrac{dy}{dx}$ and any other suggestions or typos.
karush
Gold Member
MHB
211(DOY)
If If $y=x \sin x,$ then $\dfrac{dy}{dx}=$
(A) $\sin x + \cos x$
(B) $\sin x + x \cos x$
(C) $\sin x + \cos x$
(D) $x(\sin x + \cos x)$
(E) $x(\sin x - \cos x)$
Solution
note: $y'=\dfrac{dy}{dx}$
Apply the Product Rule $$(f\cdot g)'=f\:'\cdot g+f\cdot g'$$
then
$$y'=x'\sin x+(\sin x)' x$$
simplify
$$y'=\sin x+x\cos x \quad (B)$$

ok this is a relatively simple problem but was wondering if $y'$ should be used in combination with $\dfrac{dy}{dx}=$
also any other typos ,, suggestion,, etc

karush said:
211(DOY)
If If $y=x \sin x,$ then $\dfrac{dy}{dx}=$
(A) $\sin x + \cos x$
(B) $\sin x + x \cos x$
(C) $\sin x + \cos x$
(D) $x(\sin x + \cos x)$
(E) $x(\sin x - \cos x)$
Solution
note: $y'=\dfrac{dy}{dx}$
Apply the Product Rule $$(f\cdot g)'=f\:'\cdot g+f\cdot g'$$
then
$$y'=x'\sin x+(\sin x)' x$$
simplify
$$y'=\sin x+x\cos x \quad (B)$$

ok this is a relatively simple problem but was wondering if $y'$ should be used in combination with $\dfrac{dy}{dx}=$
also any other typos ,, suggestion,, etc
It looks good. If you are given $$\displaystyle \dfrac{dy}{dx}$$ in the problem statement then I would stick with that notation.

-Dan

## 1. What is the purpose of a "2.2.211 AP Calculus Exam practice problem"?

The purpose of a "2.2.211 AP Calculus Exam practice problem" is to help students prepare for the AP Calculus Exam by providing them with practice questions that are similar to the ones they will encounter on the actual exam.

## 2. How can I access "2.2.211 AP Calculus Exam practice problems"?

"2.2.211 AP Calculus Exam practice problems" can be accessed through various online sources, such as official AP exam preparation websites or study materials provided by teachers or tutors.

## 3. Are "2.2.211 AP Calculus Exam practice problems" representative of the actual exam?

Yes, "2.2.211 AP Calculus Exam practice problems" are designed to be representative of the actual exam. They cover the same topics and follow a similar format to the questions on the AP Calculus Exam.

## 4. How can I use "2.2.211 AP Calculus Exam practice problems" effectively?

The best way to use "2.2.211 AP Calculus Exam practice problems" is to treat them as you would the actual exam questions. Time yourself and try to solve them under timed conditions to simulate the exam experience. Also, make sure to review your answers and understand any mistakes you make.

## 5. Can "2.2.211 AP Calculus Exam practice problems" guarantee a passing score on the exam?

No, "2.2.211 AP Calculus Exam practice problems" cannot guarantee a passing score on the exam. They are intended to help students prepare and familiarize themselves with the types of questions they will encounter, but ultimately, success on the exam depends on the individual's understanding and mastery of the subject material.

Replies
1
Views
1K
Replies
1
Views
988
Replies
4
Views
2K
Replies
2
Views
1K
Replies
7
Views
2K
Replies
3
Views
2K
Replies
6
Views
1K
Replies
6
Views
2K
Replies
4
Views
1K
Replies
4
Views
2K