Exploring Derivatives and the Chain Rule in AP Calculus AB

The video session begins with an introduction to the AP Calculus review, focusing on derivatives. It includes a warm-up exercise, followed by solving various practice problems. The session also covers free response questions and provides tips for exam preparation. The instructors emphasize the importance of understanding derivative rules and practicing regularly to succeed in the AP Calculus exam.

What is the derivative of sine?

• Sine

• Cosine

• Tangent

• Secant

Given dy/dx = x^3 + 2x^5, what is the value of d^3y/dx^3 at x = 2?

• 320

• 332

• 350

• 340

If h(x) = 8/(x^2 + 2x - 4), what is h'(-2)?

• 6

• 4

• 2

• 8

What is the derivative of y = 5^x + x^5 + e^(5x)?

• 5^x ln(5) + 5x^4 + 5e^(5x)

• 5^x + 5x^4 + 5e^(5x)

• 5^x + x^4 + 5e^(5x)

• 5^x ln(5) + 5x^4 + e^(5x)

If y = sqrt(cos(2x)), what is dy/dx?

• -2sin(2x) / sqrt(cos(2x))

• -sin(2x) / sqrt(cos(2x))

• -2sin(2x) / cos(2x)

• -sin(2x) / cos(2x)

What is the second derivative of cosine t?

• positive sine t

• cosine t

• negative sine t

• negative cosine t

How do you find the slope of the tangent line to the graph of a function at a given point?

• By finding the first derivative

• By finding the integral

• By finding the second derivative

• By finding the limit

What is the second derivative of a linear segment?

• It is equal to the first derivative

• It is always zero

• It is equal to the slope of the segment

• It is undefined

Which rule is used to differentiate a function that is a quotient of two other functions?

• Power rule

• Product rule

• Chain rule

• Quotient rule

What is the derivative of an inverse function at a point?

• The square of the derivative of the original function

• The negative of the derivative of the original function

• The same as the derivative of the original function

• The reciprocal of the derivative of the original function at the corresponding point