AP Calculus AB

• What is the name of the student in the study material?

  Asal
• What is the ID number of the student?


  1
• What is the date mentioned in the study material?

  10/11/19
• What period is indicated in the study material?


  9th
• What subject is being practiced in the study material?

  Calculus
• What is the task described in the study material regarding the graph of *f(x)*?

  • Sketch an approximate graph of *f’(x)* based on the graph of *f(x)*.
• What are the steps indicated for graphing derivatives?

  1. Given the graph of *f(x)*.
  2. Sketch an approximate graph of *f’(x)*.
• The derivative of sin(x) is cos(x).
• What is the first function to differentiate in the quiz?


  f(x) = x^3 + 4x^2 - 4x + 1
• What is the derivative of the function $f(x) =$$x^3 +$$4x^2 - 4x +$$1$?


  $f'(x) =$$3x^2 +$$8x - 4$
• What is the second function to differentiate in the quiz?


  y = 4x^3 - 3x^2 - 9
• What is the derivative of the function $y =$$4x^3 - 3x^2 - 9$?


  $y' =$$12x^2 - 6x$
• What is the third function to differentiate in the quiz?


  y = \frac{x^4}{2x^2} - 3
• What is the derivative of the function $y =$$\frac{x^4}{2x^2} - 3$?


  $y' =$$\frac{2x^2 - 4}{2x^2} =$$\frac{x^2 - 2}{x^2}$
• What is the function for which we need to find the derivative in problem 4?


  f(x) = 6x^5 - 5x^3 + 3x^2 - 10x + 2
• What is the derivative of the function $f(x) =$$6x^5 - 5x^3 +$$3x^2 - 10x +$$2$?


  $f'(x) =$$30x^4 - 15x^2 +$$6 - 10$
• What are the steps to find the derivative of a sum of functions?


  • Use the rule: $A(x) =$$f(x) +$$g(x)$
  • Differentiate each function separately: $A'(x) =$$f'(x) +$$g'(x)$
• If $A(x) =$$f(x) +$$g(x)$, how do you find $A'(3)$?


  Calculate $A'(3) =$$f'(3) +$$g'(3)$
• What are the steps to find the derivative of a difference of functions?


  • Use the rule: $B(x) =$$f(x) - g(x)$
  • Differentiate each function separately: $B'(x) =$$f'(x) - g'(x)$
• If $B(x) =$$f(x) - g(x)$, how do you find $B'(3)$?


  Calculate $B'(3) =$$f'(3) - g'(3)$
• What are the steps to find the derivative of a product of functions?


  • Use the product rule: $k(x) =$$f(x) \cdot g(x)$
  • Differentiate: $k'(x) =$$f'(x)g(x) +$$f(x)g'(x)$
• If $k(x) =$$f(x) \cdot g(x)$, how do you find $k'(1)$?


  Calculate $k'(1) =$$f'(1)g(1) +$$f(1)g'(1)$