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INSTRUCTORS Raffi Hovasapian John Zhu
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Lecture Comments (3)

0 answers

Post by Salman Sarwar on September 28, 2014

There is a practice question that asks "Find the derivative of y = x^[1/3]"
The answer is listed as being "[1/3]x^−[1/3]" however the correct answer is [1/3]x^−[2/3].

Just wanted to clarify for anyone doing the practice questions.

1 answer

Last reply by: Manoj Sharma
Wed Aug 20, 2014 2:08 PM

Post by Manoj Sharma on August 20, 2014

Hey guys I was wondering on Example 3, If n should actually be -1. Since n-1= -2, then you would add 1 both sides and get the answer of -1. Please let me know if I am wrong.

Power Rule

  • Power rule:
  • To avoid confusion, treat n as just a constant
  • Misleading constants: natural logs, fractions, and decimals

Power Rule

Find the derivative of y = 2x3 + 5x2 + 7x + 11
  • dy = [d/dx] (2x3 + 5x2 + 7x + 11)
  • = 2[d/dx] x3 + 5 [d/dx] x2 + 7 [d/dx] x
  • = 2(3x2) + 5(2x) + 7(1) =
6x2 + 10x + 7
Find the derivative of y = x[1/3]
  • dy = [d/dx] x[1/3]
[1/3] x−[1/3]
Find the derivative of y = (x + 4)2
  • dy = [d/dx] (x + 4)2
  • = [d/dx] (x2 + 8x + 16)=
2x + 8
Find the derivative of y = √2 x2
  • dy = [d/dx] √2 x2
  • = √2 [d/dx] x2 =
2 √2 x
Find the derivative of y = 2 √x
  • dy = [d/dx]2 √x
  • = 2 [d/dx] √x
  • = 2 [d/dx] x[1/2]
  • = 2 [1/2] x−[1/2]
  • = x−[1/2] =
[1/(√x)]
Find the derivative of y = [(x3)/(x[1/3])]
  • dy = [d/dx] [(x3)/(x[1/3])]
  • = [d/dx] x3 x−[1/3]
  • = [d/dx] x(3 − [1/3])
  • = [d/dx] x[8/3]
[8/3] x[5/3]
Find the derivative of y = (√x + 1)2
  • dy = [d/dx] (√x + 1)2
  • = [d/dx] (x + 2√x + 1)
= 1 + x−[1/2]
Find the derivative of y = x − [(x3)/3!] + [(x5)/5!]
  • dy = [d/dx] (x − [(x3)/3!] + [(x5)/5!])
  • = 1 − [(3x2)/3!] + [(5x4)/5!]
1 − [(x2)/2!] + [(x4)/4!]
NOTE: y in this problem is a truncated version of the series representation of sin(x).
Find the derivative of y = 1 − [(x2)/2!] + [(x4)/4!] − [(x6)/6!]
  • dy = [d/dx] (1 − [(x2)/2!] + [(x4)/4!] − [(x6)/6!])
  • = 0 − [2x/2!] + [(4x3)/4!] − [(6x5)/6!]
−x + [(x3)/3!] − [(x5)/5!]
NOTE: y in this problem is a truncated version of the series representation of cos(x).
Find the derivative of y = 1 + x + [(x2)/2!] + [(x3)/3!] + [(x4)/4!]
  • dy = [d/dx] (1 + x + [(x2)/2!] + [(x3)/3!] + [(x4)/4!])
1 + x + [(x2)/2!] + [(x3)/3!]
NOTE: y in this problem is a truncated version of the series representation of ex.

*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

Power Rule

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
  • Power Rule 0:07
    • Power Rule Definition
  • Example 1 1:11
  • Example 2 2:25
  • Example 3 3:05
  • Example 4 4:18
  • Example 5 5:13