Results 1 to 8 of 8

Math Help - Help with derivatives

  1. #1
    Newbie
    Joined
    Jul 2014
    From
    some where
    Posts
    6

    Help with derivatives

    Hi, I'm not sure if I'm doing the right way. Here is the problems

    1. sqrt (6x+5) (Get the derivative using this formulate f(x) = ((x+h) - x)/h ) lim h-> 0 so this is my attemp.

    [ sqrt(6(x+h)+5) - sqrt(6x+5) ] / h

    then I rationalize the numerator

    (6x+6h+5 - 6x-5 ) / h(sqrt(6x+6h+5)(sqrt(6x+5)

    then I simplify the numberator

    6h / h(sqrt(6x+6h+5)(sqrt(6x+5)

    can you tell me what i am doing the right way or show me how to do it.


    2. the second is the product rule of derivative (sqrt(x) + 3x)(5x^2 - 3/x)

    apply the rule,

    (1/2 x^-1/2 + 3)(5x^2 - 3/x) + (sqrt(x) + 3x)(10x + 3/x^2)

    then i put down the negative power to denominator
    (1/(2 sqrt(x)) + 3)(5x^2 - 3/x) + (sqrt(x) + 3x)(10x + 3/x^2)

    then what should i do next? or show me the next step.


    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602

    Re: Help with derivatives

    For 1 you have done everything correctly, so now cancel off the factor of h from the top and bottom and then make h -> 0.

    For 2 you have done enough. If you REALLY want to you could get a common denominator and try to simplify, but the idea is that you are trying to find a correct derivative, which you have already done.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2014
    From
    some where
    Posts
    6

    Re: Help with derivatives

    Quote Originally Posted by Prove It View Post
    For 1 you have done everything correctly, so now cancel off the factor of h from the top and bottom and then make h -> 0.

    For 2 you have done enough. If you REALLY want to you could get a common denominator and try to simplify, but the idea is that you are trying to find a correct derivative, which you have already done.
    I manage to get the answer in 2. but what do you mean cancel off the factor of h? can you show me. thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602

    Re: Help with derivatives

    You've ended up with $\displaystyle \begin{align*} \frac{6h}{h\left( \sqrt{6x + 6h + 5} + \sqrt{6x + 5} \right) } \end{align*}$. Surely you can see something you can cancel...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2014
    From
    some where
    Posts
    6

    Re: Help with derivatives

    Quote Originally Posted by Prove It View Post
    You've ended up with $\displaystyle \begin{align*} \frac{6h}{h\left( \sqrt{6x + 6h + 5} + \sqrt{6x + 5} \right) } \end{align*}$. Surely you can see something you can cancel...
    can i cancel the h in top and bottom, then limit h->0 then i will have 6 / ((sqrt (6x + 5) + sqrt(6x+5)) . and is there a + sign in th denominator of two sqrt?

    sorry. im not really good at math
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,831
    Thanks
    1602

    Re: Help with derivatives

    Yes that's right. And yes you need the + sign there, because to rationalise the numerator of $\displaystyle \begin{align*} \sqrt{6x + 6h + 5} - \sqrt{6x + 5} \end{align*}$ you need to multiply top and bottom by $\displaystyle \begin{align*} \sqrt{6x + 6h + 5} + \sqrt{ 6x + 5} \end{align*}$.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jul 2014
    From
    some where
    Posts
    6

    Re: Help with derivatives

    Quote Originally Posted by Prove It View Post
    Yes that's right. And yes you need the + sign there, because to rationalise the numerator of $\displaystyle \begin{align*} \sqrt{6x + 6h + 5} - \sqrt{6x + 5} \end{align*}$ you need to multiply top and bottom by $\displaystyle \begin{align*} \sqrt{6x + 6h + 5} + \sqrt{ 6x + 5} \end{align*}$.
    thanks alot.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Jul 2014
    From
    Waterloo, ON
    Posts
    82
    Thanks
    18

    Re: Help with derivatives

    Quote Originally Posted by Prove It View Post
    Yes that's right. And yes you need the + sign there, because to rationalise the numerator of $\displaystyle \begin{align*} \sqrt{6x + 6h + 5} - \sqrt{6x + 5} \end{align*}$ you need to multiply top and bottom by $\displaystyle \begin{align*} \sqrt{6x + 6h + 5} + \sqrt{ 6x + 5} \end{align*}$.
    I thought it's okay to plug in h=0 at this point though... Although it's technically h->0, what i was taught with was, you can straight up plug in h=0 if nothing will go wrong because of that.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: November 12th 2012, 01:55 AM
  2. Derivatives and Anti-Derivatives
    Posted in the Calculus Forum
    Replies: 7
    Last Post: February 6th 2011, 07:21 AM
  3. Replies: 1
    Last Post: July 19th 2010, 05:09 PM
  4. Replies: 4
    Last Post: February 10th 2009, 10:54 PM
  5. Trig derivatives/anti-derivatives
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 10th 2009, 02:34 PM

Search Tags


/mathhelpforum @mathhelpforum