Results 1 to 4 of 4

Math Help - Differentiation

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    5

    Differentiation

    Could someone please help me out with these differentiation questions. Thanks.

    determine f'(x) of f(x) = [4rt(x2+4)]^3
    dy/dx of:
    y=x^2(x-3)^5
    y=3x(x+1)^3+3
    y=2x(x^2+3)^4

    The isosceles triangle has sides AC and AB of equal length and each increasing at 0.1cm/sec from an initial 5cm. Find the rate of change in the area of triangle ABC at the instant when AC=AB=10cm.

    The length of a particular rectangle is three times its width and this ratio is maintained as the width is increased at 1mm/sec. Find the rate of increase in the area of the rectangle when the width is 10cm.

    A right angle triangle has sides AB and BC able to vary in length, AC is constantly 10cm long and angle ABC is always a right angle. Initially AB is of length 4cm and increases at a constant rate of 0.1cm/sec. Find the rate of change in the length of BC, 20 seconds after the increasing in the length of AB commenced.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Quote Originally Posted by Mickey View Post
    Could someone please help me out with these differentiation questions. Thanks.

    determine f'(x) of f(x) = [4rt(x2+4)]^3
    dy/dx of:
    y=x^2(x-3)^5
    y=3x(x+1)^3+3
    y=2x(x^2+3)^4
    People here at MHF are not fond of those who post a whole bunch of questions piled up into one post. I will start off by helping you with the chain rule for the first of these questions. With that, you should be able to do the 2nd, 3rd and 4th problems.

    f(x) = [4rt(x^2+4)]^3

    Apply the chain rule when deriving this function.

    f'(x)=3[4rt(x^2+4)]^2 * ???

    Those question marks are to be filled with what you are supposed to tack on for the chain rule. When a function has functions nested in it like so: f=g(h), then the derivative follows through like a chain: f'=g'(h)*h'

    Therefore....

    f'(x)=3[4rt(x^2+4)]^2 * ??? \Rightarrow 3[4rt(x^2+4)]^2 4rt(2x) = 24rtx[4rt(x^2+4)]^2

    Remember one last thing here; you are deriving with respect to x. Other variables are then treated as constants, hence why the "r" and "t" followed through as coefficients.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by colby2152 View Post
    People here at MHF are not fond of those who post a whole bunch of questions piled up into one post. [snip]
    Hmmmmmm, not to mention a lack of thanks for any of the replies given to date.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hi,

    ...and people who just ask their question then never come back :'(
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 26th 2010, 06:24 PM
  2. Differentiation and partial differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 30th 2010, 11:16 PM
  3. Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 4th 2010, 11:45 AM
  4. Differentiation Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 25th 2010, 07:20 PM
  5. Differentiation and Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 6th 2009, 05:07 AM

Search Tags


/mathhelpforum @mathhelpforum