Parital derivation

Discussion in 'Math' started by mo2015mo, May 11, 2013.

  1. mo2015mo

    Thread Starter Member

    May 9, 2013
    157
    1
    Hi guys :) ,

    I have been having problems with the attached question, I have tried to solve it But don't get the correct answer
    i want to know HOW can derive the function under the root square
    plz help meee
     
  2. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    How come this isn't in homework?

    Have you heard of implicit differentiation?

    Square both sides, for example

    {y^2} = uv

    Differentiate with respect to u, holding v constant.


    \begin{array}{l}<br />
 2y\frac{{\partial y}}{{\partial u}} = \frac{{\partial (uv)}}{{\partial u}} = v \\ <br />
 \frac{{\partial y}}{{\partial u}} = \frac{v}{{2y}} = \frac{v}{{2\sqrt {uv} }} = \frac{{\sqrt v }}{{2\sqrt u }} \\ <br />
 \end{array}

    If you are not familiar with implicit differentiaion, you can do this one the ordinary way as follows


    y = \sqrt {uv}  = {u^{\frac{1}{2}}}{v^{\frac{1}{2}}}

    Differentiate with respect to u, holding v constant.

    \begin{array}{l}<br />
 y = \sqrt {uv}  = {u^{\frac{1}{2}}}{v^{\frac{1}{2}}} \\ <br />
 \frac{{\partial y}}{{\partial u}} = \frac{1}{2}{u^{ - \frac{1}{2}}}{v^{\frac{1}{2}}} = \frac{{\sqrt v }}{{2\sqrt u }} \\ <br />
 \end{array}

    As before.

    In this instance implicit differentiation offers no real advantages, but sometimes it is the only way and often it is the easiest way with a square root involved.

    Does this help?
     
    Last edited: May 12, 2013
    mo2015mo likes this.
  3. mo2015mo

    Thread Starter Member

    May 9, 2013
    157
    1
    yes yes i have heard of implicit differentiation ,But it did not come into My mind :(
    Studiot
    Thank you so much for all you’ve done to help me :)
     
  4. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    Presumably you can finish all the rest off now?
     
  5. mo2015mo

    Thread Starter Member

    May 9, 2013
    157
    1
    yes, i have solved the rest and gotten the correct answer

    Thanks again for help me :) :)
     
  6. WBahn

    Moderator

    Mar 31, 2012
    17,715
    4,788
    Good. I would recommend doing them directly, as well, and verifying that you get the same answers.
     
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