Results 1 to 7 of 7

Math Help - derrivative

  1. #1
    Member
    Joined
    Jun 2007
    Posts
    120

    derrivative

    r(t)=(t+e^t)(3-[sqrt(t)])

    find r'(t)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    Recall the product rule: \big[ f(t)g(t) \big]' = {\color{red}f'(t)}g(t) + f(t){\color{blue}g'(t)}

    Here imagine: f(t) = t + e^t and g(t) = 3 - \sqrt{t}

    So plugging in we have: \big[ (t+e^t)(3-\sqrt{t}) \big]' = {\color{red}(t + e^t)'}(3-\sqrt{t}) + (t+e^t){\color{blue}(3 - \sqrt{t})'}

    Now it's just a matter of finding the derivatives of the red and the blue which should be pretty straightforward.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2008
    Posts
    46
    Hi,

    The best approach is to use the product rule here, with u=(t+e^t) and v=(3-sqrt(t)).

    The derivative should then be easily calculated.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jun 2007
    Posts
    120
    yeah, its just that i got the derrivatives, but now when i try to simplify im stuck, because i dont know how to multiply e^t with anything.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    Show us what you've got.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Jun 2007
    Posts
    120
    sorry but i dont know latex so i know this will be hard to read but...

    r'(t)= (1+e^t)[3-sqrt(t)] + (t+e^t)(1/2t^(-1/2))

    its like how would i multiply e^t and t^(1/2) together? and where e^t would need to be multiplied. i just dont know how to simplify further.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    With product rule questions, you are usually not expected to simplify that much.

    As for your question, you can't multiply e^t and \sqrt{t} together to get anything new so you just simply leave it as e^t\sqrt{t}

    So, just multiplying out the brackets:
    \begin{array}{rcl}r'(t) & = & (1 + e^t)(3-\sqrt{t}) + (t + e^t )\displaystyle \left(\frac{1}{2\sqrt{t}}\right) \\ & & \\ & = & \displaystyle 3 - \sqrt{t} + 3e^t - e^t\sqrt{t} + {\color{blue}\frac{t}{2\sqrt{t}}} + \frac{e^{t}}{2\sqrt{t}} \end{array}

    You can do a bit of simplifying (simplify the blue and see if you can combine it with another term) or combine like terms another way. Either way your final answer isn't going to look all that much neater
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Derrivative
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 23rd 2008, 08:38 AM
  2. derrivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 15th 2008, 08:43 PM
  3. derrivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 13th 2008, 12:05 PM
  4. Second Derrivative
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 20th 2008, 11:41 AM
  5. Derrivative
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 24th 2007, 11:21 AM

Search Tags


/mathhelpforum @mathhelpforum