1997 AP Calculus BC Multiple Choice Question 10 Solution

In this video, we will solve a 1997 AP Calculus BC Multiple Choice Question 10 that states "If x*y + x² + 1 and x = -1, find dy/dx." To approach this problem, we need to use implicit differentiation since x and y are multiplied together.

We start by taking the derivative of y with respect to x (y') using implicit differentiation. For the right side of the equation, we need to use the product rule since y is a function of x. After simplifying and solving for y', we get the following equation

y' = (y + 2x)/(1 - x)

Next, we need to evaluate this derivative at x = -1. However, we don't know the value of y at x = -1, so we need to find it first. We can do this by substituting x = -1 in the original equation and solving for y. We get y = -1 + 2, which is y = 1.

Now, we can substitute x = -1 and y = 1 in the derivative equation and simplify to get the final answer. The correct answer is -1/2, which is choice (b) in the answer choices.

This video provides a step-by-step solution to a challenging AP Calculus BC problem and explains how to approach similar problems. It is an excellent resource for students preparing for calculus exams or anyone interested in learning calculus.

📚 Keywords AP Calculus BC, Multiple Choice Question, Implicit Differentiation, Derivatives, Product Rule, Calculus Exams

🤔 Internet Questions

1️⃣ What is implicit differentiation?
- Implicit differentiation is a method used to find the derivative of a function that is not explicitly defined.

2️⃣ How do you solve an AP Calculus BC Multiple Choice Question?
- To solve an AP Calculus BC Multiple Choice Question, you need to apply the appropriate calculus concepts and techniques to find the correct answer.

3️⃣ What is the product rule in calculus?
- The product rule is a formula used to find the derivative of a product of two functions.

4️⃣ What is a derivative?
- A derivative is a mathematical expression that represents the rate of change of a function with respect to its independent variable.

5️⃣ What is the AP Calculus BC exam?
- The AP Calculus BC exam is a standardized test administered by the College Board that assesses students' knowledge of calculus concepts and techniques.

6️⃣ How do you prepare for the AP Calculus BC exam?
- To prepare for the AP Calculus BC exam, you need to study calculus concepts and techniques, practice solving problems, and take practice tests.

7️⃣ What is the difference between AP Calculus AB and BC?
- AP Calculus AB covers calculus concepts up to derivatives and integrals, while AP Calculus BC covers more advanced calculus topics such as series, parametric equations, and polar coordinates.

8️⃣ What is a polar coordinate system?
- A polar coordinate system is a two-dimensional coordinate system in which each point is determined by a distance from a fixed point and an angle from a fixed direction.

9️⃣ What is a series in calculus?
- A series in calculus is a sum of an infinite sequence of numbers or functions.

🔟 What is a parametric equation?
- A parametric equation is a set of equations that defines a curve or surface in terms of one or more parameters.

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