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INSTRUCTORS Raffi Hovasapian John Zhu
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For more information, please see full course syllabus of Calculus AB
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Lecture Comments (7)

1 answer

Last reply by: John Zhu
Mon Aug 12, 2013 9:21 PM

Post by Malachy Uchechuwkwu Orji on September 4, 2012

Don't you think the expression should be solved further to arrive at the final answer rather than leaving behind the d/dx notation,atleast for the sake of the weak ones.

2 answers

Last reply by: John Zhu
Mon Aug 12, 2013 9:21 PM

Post by Malachy Uchechuwkwu Orji on September 4, 2012

i think the (d/dx *2x) = 2 and not 1.

1 answer

Last reply by: Him Tam
Wed Sep 4, 2013 10:39 PM

Post by James Xie on June 27, 2012

For the example, (d/dx)(x^2 - 2x), shouldn't the answer be (d/dx)(x^2) - 2 instead of minus 1?

Basic Rules of Differentiation

  • Know very well. This is the foundation for more advanced derivatives.
  • Constant rule:
  • Constant multiple rule:
  • Addition and difference rule:

Basic Rules of Differentiation

Solve [d/dx] (92828237 + √{13})
  • [d/dx] 92828237 + [d/dx] √{13} = 0 + 0 =
0
Simplify [d/dx] 3x2
[d/dx] 3x2 = 3 [d/dx] x2
Simplify [d/dx] (5x3 + 12)
  • [d/dx] (5x3 + 12) = [d/dx] 5x3 + [d/dx] 12
  • = 5 [d/dx] x3 + 0
5 [d/dx] x3
Simplify [d/dx] (5cos(3x) + 4x)
[d/dx] (5cos(3x) + 4x) = 5 [d/dx] cos(3x) + 4 [d/dx] x
Simplify [d/dx] ex + 1
[d/dx] ex + 1 = [d/dx] ex e1 = e1 [d/dx] ex
Simplify [d/dx] ln(5)
[d/dx] ln(5) = 0
Simplify [d/dx] (x + 3)2
  • [d/dx] (x + 3)2 = [d/dx] (x2 + 6x + 9)
  • = [d/dx] x2 + [d/dx] 6x + [d/dx] 9
= [d/dx] x2 + 6 [d/dx] x
Simplify [d/dx] ([(x2 + 5x + 6)/(x + 2)])
  • [d/dx] ([(x2 + 5x + 6)/(x + 2)]) = [d/dx] ([((x + 3)(x + 2))/(x + 2)])
  • = [d/dx] (x + 3) = [d/dx] x
x
Simplify [d/dx] (e5 + e5x + sin(π))
  • [d/dx] (e5 + e5x + sin(π)) = [d/dx] e5 + [d/dx] e5x + [d/dx] sin(π)
  • = [d/dx] e5x
[d/dx] e5x
Simplify [d/dx] e7 sin(5x2)
  • [d/dx] e7 sin(5x2) = e7 [d/dx] sin(5x2)
e7 [d/dx] sin(5x2)

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Basic Rules of Differentiation

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Basic Rules of Differentiation 0:09
  • Constant Rule 0:14
  • Constant Multiple Rule 1:10
  • Addition and Difference Rule 1:40
  • Example 1: Constant Rule 2:25
  • Example 2: Constant Multiple Rule 3:01
  • Example 3: Constant Multiple Rule 3:35
  • Example 4: Constant Rule 4:34
  • Example 5: Constant Multiple Rule 5:03
  • Example 6 5:33