Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By Soroban

Math Help - Product/Quotient rule?

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    UK
    Posts
    5

    Product/Quotient rule?

    Given that x \sqrt{1+2x}


    Show that \frac{dy}{dx} =  (1+3x)/\sqrt {1+2x}


    First, off, do I use the product rule of quotient rule. Second, could you show me how you got the answer? I got loads more but if you show me how to do one, I think I'll pick up on the rest. Any help is really appreciated, I'm so confused.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    644

    Re: Product/Quotient rule?

    Hello, EarlyTravel!

    Given that: . y \:=\:x \sqrt{1+2x}

    Show that: . \frac{dy}{dx} \:=\:  \frac{1+3x}{\sqrt {1+2x}}

    Since we have a product: . y \:=\:x\cdot (1 + 2x)^{\frac{1}{2}}, of course we use the Product Rule.

    Do you know the Product Rule?

    If y \:=\:f(x)\!\cdot\!g(x), then: . \frac{dy}{dx} \:=\:f'(x)\!\cdot\!g(x) + f(x)\!\cdot\!g'(x)


    \text{We have: }\:y \;=\;\underbrace{x}_{f(x)}\cdot\underbrace{(1+2x)^  {\frac{1}{2}}}_{g(x)}

    \text{Hence: }\:\frac{dy}{dx} \;=\;\underbrace{1}_{f'(x)}\cdot\underbrace{(1+2x)  ^{\frac{1}{2}}}_{g(x)} + \underbrace{x}_{f(x)}\cdot\underbrace{\tfrac{1}{2}  (1+2x)^{\text{-}\frac{1}{2}}\cdot 2}_{g'(x)}

    . . . . . . . . =\;(1 +2x)^{\frac{1}{2}} + x(1 + 2x)^{\text{-}\frac{1}{2}}

    . . . . . . . . =\;\sqrt{1+2x} + \frac{x}{\sqrt{1+2x}}

    . . . . . . . . =\;\frac{\sqrt{1+2x}}{1}\cdot {\color{blue}\frac{\sqrt{1+2x}}{\sqrt{1+2x}}} + \frac{x}{\sqrt{1+2x}}

    . . . . . . . . =\;\frac{1+2x}{\sqrt{1+2x}} + \frac{x}{\sqrt{1+2x}}

    . . . . . . . . =\;\frac{(1+2x) + x}{\sqrt{1+2x}}

    . . . . . . . . =\;\frac{1+3x}{\sqrt{1+2x}}
    Thanks from EarlyTravel
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    UK
    Posts
    5

    Re: Product/Quotient rule?

    Thank you SO much, honestly, you're a life saver.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: December 20th 2011, 04:57 AM
  2. Quotient / Product Rule help
    Posted in the Calculus Forum
    Replies: 9
    Last Post: October 10th 2010, 06:53 PM
  3. Proof for Product Rule and Quotient Rule
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: August 24th 2010, 01:35 AM
  4. Product and Quotient Rule Help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 18th 2009, 05:25 PM
  5. Product and Quotient Rule
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 27th 2008, 08:12 PM

Search Tags


/mathhelpforum @mathhelpforum