Important Announcement(s)
Congratulations to
heredia21

Select a forum to post in:

Derivatives

Math topics

Moderators: Jessica, Teachers

Looking for a topic?
View the Math Topics Directory to find topics quicker under different kinds of math.

Derivatives

Post Number: #1  Postby Jessica » August 24th, 2011, 1:04 pm

The derivative of Image with respect to x is the function Image and is defined as,
Image



Example
Image


First plug the function into the definition of the derivative.
Image

Multiply everything out
Image

Image

So the derivative is
Image
  • 0

User avatar
Jessica
Board Owner
Topic Author

Founder
Sapphire
Sapphire
 
7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership
 
Posts: 3,461
Topics: 1,244
Articles: 30
Joined: December 22nd, 2010, 8:04 pm
Local time: November 18th, 2018, 5:37 am
Last Visit: Today, 12:11 am
Location: Pennsylvania
Gender: Female
Cash on hand: 4,596.17
Bank: 132,045.08
Reputation: 148
Medals: 19
#1: July 2012 1st Place (1) R-Contest #1 First Place (1) Best staff member 2013 (1) Easter Egg Hunt 2013 (1) Graphic Drawing Participant (1) 1 Year (1) 2 Years (1) 3 Years (1) 4 Years (1) 5 Years (1)
6 Years (1) 7 Years (1) Founder (1) Highest Rep (1) Referrer (1) Top poster (1) Facebook group (1) Pin-Board (1) Article Author (1)
Referrals: 27
Blog: View Blog (463)
Subject(s): Chinese, Math
Global Moderator
Admin
Moderator

Re: Derivatives

Post Number: #2  Postby Jessica » October 18th, 2011, 10:08 pm

this is the alternate definition of the derivative.

  • 0

User avatar
Jessica
Board Owner
Topic Author

Founder
Sapphire
Sapphire
 
7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership
 
Posts: 3,461
Topics: 1,244
Articles: 30
Joined: December 22nd, 2010, 8:04 pm
Local time: November 18th, 2018, 5:37 am
Last Visit: Today, 12:11 am
Location: Pennsylvania
Gender: Female
Cash on hand: 4,596.17
Bank: 132,045.08
Reputation: 148
Medals: 19
#1: July 2012 1st Place (1) R-Contest #1 First Place (1) Best staff member 2013 (1) Easter Egg Hunt 2013 (1) Graphic Drawing Participant (1) 1 Year (1) 2 Years (1) 3 Years (1) 4 Years (1) 5 Years (1)
6 Years (1) 7 Years (1) Founder (1) Highest Rep (1) Referrer (1) Top poster (1) Facebook group (1) Pin-Board (1) Article Author (1)
Referrals: 27
Blog: View Blog (463)
Subject(s): Chinese, Math
Global Moderator
Admin
Moderator

Re: Derivatives

Post Number: #3  Postby Jessica » October 23rd, 2011, 9:01 pm

  • 0

User avatar
Jessica
Board Owner
Topic Author

Founder
Sapphire
Sapphire
 
7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership
 
Posts: 3,461
Topics: 1,244
Articles: 30
Joined: December 22nd, 2010, 8:04 pm
Local time: November 18th, 2018, 5:37 am
Last Visit: Today, 12:11 am
Location: Pennsylvania
Gender: Female
Cash on hand: 4,596.17
Bank: 132,045.08
Reputation: 148
Medals: 19
#1: July 2012 1st Place (1) R-Contest #1 First Place (1) Best staff member 2013 (1) Easter Egg Hunt 2013 (1) Graphic Drawing Participant (1) 1 Year (1) 2 Years (1) 3 Years (1) 4 Years (1) 5 Years (1)
6 Years (1) 7 Years (1) Founder (1) Highest Rep (1) Referrer (1) Top poster (1) Facebook group (1) Pin-Board (1) Article Author (1)
Referrals: 27
Blog: View Blog (463)
Subject(s): Chinese, Math
Global Moderator
Admin
Moderator

Re: Derivatives

Post Number: #4  Postby Jessica » October 23rd, 2011, 9:02 pm

Rule 1: Derivative of a Constant

If c is a constant, then




Rule 2: Power Rule for a Positive Integer Powers of x

If n is a positive integer, then nxn−1




Rule 3: The Constant Multiple Rule

If u is a differentiable function of x and c is a constant, then




Rule 4: The Sum and Difference Rule

If u and v are differentiable functions of x, then their sum and differences are differentiable at every point where u and v are both differentiable. At such points,

1.


2.




Rule 5: The Product Rule

If the products of two differentiable functions u and v is differentiable and...

    u = first factorv = second factor




(first) · (second)' + (second) · (first)'



Finding Horizontal Tangents:

Horizontal tangents occur when the slope of the derivative equals zero.





Rule 6: The Quotient Rule

At a point where v ≠ 0, the quotient of two differentiable functions is differentiable and...

u = numerator part of quotient
v = denominator part of quotient


  • 0

User avatar
Jessica
Board Owner
Topic Author

Founder
Sapphire
Sapphire
 
7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership
 
Posts: 3,461
Topics: 1,244
Articles: 30
Joined: December 22nd, 2010, 8:04 pm
Local time: November 18th, 2018, 5:37 am
Last Visit: Today, 12:11 am
Location: Pennsylvania
Gender: Female
Cash on hand: 4,596.17
Bank: 132,045.08
Reputation: 148
Medals: 19
#1: July 2012 1st Place (1) R-Contest #1 First Place (1) Best staff member 2013 (1) Easter Egg Hunt 2013 (1) Graphic Drawing Participant (1) 1 Year (1) 2 Years (1) 3 Years (1) 4 Years (1) 5 Years (1)
6 Years (1) 7 Years (1) Founder (1) Highest Rep (1) Referrer (1) Top poster (1) Facebook group (1) Pin-Board (1) Article Author (1)
Referrals: 27
Blog: View Blog (463)
Subject(s): Chinese, Math
Global Moderator
Admin
Moderator

Re: Derivatives

Post Number: #5  Postby Jessica » November 12th, 2011, 12:39 pm

Derivatives of the Six Trig Functions











  • 0

User avatar
Jessica
Board Owner
Topic Author

Founder
Sapphire
Sapphire
 
7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership
 
Posts: 3,461
Topics: 1,244
Articles: 30
Joined: December 22nd, 2010, 8:04 pm
Local time: November 18th, 2018, 5:37 am
Last Visit: Today, 12:11 am
Location: Pennsylvania
Gender: Female
Cash on hand: 4,596.17
Bank: 132,045.08
Reputation: 148
Medals: 19
#1: July 2012 1st Place (1) R-Contest #1 First Place (1) Best staff member 2013 (1) Easter Egg Hunt 2013 (1) Graphic Drawing Participant (1) 1 Year (1) 2 Years (1) 3 Years (1) 4 Years (1) 5 Years (1)
6 Years (1) 7 Years (1) Founder (1) Highest Rep (1) Referrer (1) Top poster (1) Facebook group (1) Pin-Board (1) Article Author (1)
Referrals: 27
Blog: View Blog (463)
Subject(s): Chinese, Math
Global Moderator
Admin
Moderator

Re: Derivatives

Post Number: #6  Postby Jessica » November 16th, 2011, 12:26 am

Chain Rule

useful when asked to find the derivative of compositions such as


Method 1: "outside-inside" rule

   •    ( 2 )
deriv of outside      deriv of inside
leave inside alone





Method 2:

Examples coming soon
  • 0

User avatar
Jessica
Board Owner
Topic Author

Founder
Sapphire
Sapphire
 
7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership
 
Posts: 3,461
Topics: 1,244
Articles: 30
Joined: December 22nd, 2010, 8:04 pm
Local time: November 18th, 2018, 5:37 am
Last Visit: Today, 12:11 am
Location: Pennsylvania
Gender: Female
Cash on hand: 4,596.17
Bank: 132,045.08
Reputation: 148
Medals: 19
#1: July 2012 1st Place (1) R-Contest #1 First Place (1) Best staff member 2013 (1) Easter Egg Hunt 2013 (1) Graphic Drawing Participant (1) 1 Year (1) 2 Years (1) 3 Years (1) 4 Years (1) 5 Years (1)
6 Years (1) 7 Years (1) Founder (1) Highest Rep (1) Referrer (1) Top poster (1) Facebook group (1) Pin-Board (1) Article Author (1)
Referrals: 27
Blog: View Blog (463)
Subject(s): Chinese, Math
Global Moderator
Admin
Moderator

Re: Derivatives

Post Number: #7  Postby Jessica » November 19th, 2011, 10:09 pm

Finding parametrically:

  • 0

User avatar
Jessica
Board Owner
Topic Author

Founder
Sapphire
Sapphire
 
7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership
 
Posts: 3,461
Topics: 1,244
Articles: 30
Joined: December 22nd, 2010, 8:04 pm
Local time: November 18th, 2018, 5:37 am
Last Visit: Today, 12:11 am
Location: Pennsylvania
Gender: Female
Cash on hand: 4,596.17
Bank: 132,045.08
Reputation: 148
Medals: 19
#1: July 2012 1st Place (1) R-Contest #1 First Place (1) Best staff member 2013 (1) Easter Egg Hunt 2013 (1) Graphic Drawing Participant (1) 1 Year (1) 2 Years (1) 3 Years (1) 4 Years (1) 5 Years (1)
6 Years (1) 7 Years (1) Founder (1) Highest Rep (1) Referrer (1) Top poster (1) Facebook group (1) Pin-Board (1) Article Author (1)
Referrals: 27
Blog: View Blog (463)
Subject(s): Chinese, Math
Global Moderator
Admin
Moderator

Re: Derivatives

Post Number: #8  Postby Jessica » December 5th, 2011, 5:05 pm

Derivatives of Inverse Trig Functions



is exactly the same except it's negative.




is exactly the same except it's negative.




is exactly the same except it's negative.



Image
  • 0

User avatar
Jessica
Board Owner
Topic Author

Founder
Sapphire
Sapphire
 
7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership
 
Posts: 3,461
Topics: 1,244
Articles: 30
Joined: December 22nd, 2010, 8:04 pm
Local time: November 18th, 2018, 5:37 am
Last Visit: Today, 12:11 am
Location: Pennsylvania
Gender: Female
Cash on hand: 4,596.17
Bank: 132,045.08
Reputation: 148
Medals: 19
#1: July 2012 1st Place (1) R-Contest #1 First Place (1) Best staff member 2013 (1) Easter Egg Hunt 2013 (1) Graphic Drawing Participant (1) 1 Year (1) 2 Years (1) 3 Years (1) 4 Years (1) 5 Years (1)
6 Years (1) 7 Years (1) Founder (1) Highest Rep (1) Referrer (1) Top poster (1) Facebook group (1) Pin-Board (1) Article Author (1)
Referrals: 27
Blog: View Blog (463)
Subject(s): Chinese, Math
Global Moderator
Admin
Moderator

Re: Derivatives

Post Number: #9  Postby Jessica » December 8th, 2011, 8:42 am

Image

Image

note: each will be multiplied by
  • 0

User avatar
Jessica
Board Owner
Topic Author

Founder
Sapphire
Sapphire
 
7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership7 years of membership
 
Posts: 3,461
Topics: 1,244
Articles: 30
Joined: December 22nd, 2010, 8:04 pm
Local time: November 18th, 2018, 5:37 am
Last Visit: Today, 12:11 am
Location: Pennsylvania
Gender: Female
Cash on hand: 4,596.17
Bank: 132,045.08
Reputation: 148
Medals: 19
#1: July 2012 1st Place (1) R-Contest #1 First Place (1) Best staff member 2013 (1) Easter Egg Hunt 2013 (1) Graphic Drawing Participant (1) 1 Year (1) 2 Years (1) 3 Years (1) 4 Years (1) 5 Years (1)
6 Years (1) 7 Years (1) Founder (1) Highest Rep (1) Referrer (1) Top poster (1) Facebook group (1) Pin-Board (1) Article Author (1)
Referrals: 27
Blog: View Blog (463)
Subject(s): Chinese, Math
Global Moderator
Admin
Moderator


Return to Math Topics

Login  •  Register
cron
Reputation System ©'