Results 1 to 3 of 3

Math Help - Derivative Help

  1. #1
    Newbie gs.sh11's Avatar
    Joined
    Oct 2009
    Posts
    14

    Derivative Help

    Hi, Im a total newb at Calculus, Im only in Triginometry in my school, but Im trying to self-learn Calculus, and im having trouble understanding this concept of derivatives. I understand that it is the tangent of a line, and I also understand how to find them the long way using, \frac{f(x+h) - f(x)}{h}

    But my question is, is there any shortcut to finding a derivative, like in the function f(x) = x^n the derivative is simply f^1(x) = nx^n-1, but what do I do for the bigger ones such as f(x) = x^2 + 2x, is there any shortcut there? I already found the derivative of f(x) = x^2 + 2x which is \frac{x^2 + 2x}{-4x}

    So please tell me if you know any shortcuts to finding the derivatives of a function such as f(x) = x^2 + 2x. Thanks!

    P.S - Please dont use any big calculus words - im only in triginometry!
    Attached Thumbnails Attached Thumbnails Derivative Help-d-x-2-2x.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2008
    From
    Scotland
    Posts
    901
    Quote Originally Posted by gs.sh11 View Post
    Hi, Im a total newb at Calculus, Im only in Triginometry in my school, but Im trying to self-learn Calculus, and im having trouble understanding this concept of derivatives. I understand that it is the tangent of a line, and I also understand how to find them the long way using, \frac{f(x+h) - f(x)}{h}

    But my question is, is there any shortcut to finding a derivative, like in the function f(x) = x^n the derivative is simply f^1(x) = nx^n-1, but what do I do for the bigger ones such as f(x) = x^2 + 2x, is there any shortcut there? I already found the derivative of f(x) = x^2 + 2x which is \frac{x^2 + 2x}{-4x}

    So please tell me if you know any shortcuts to finding the derivatives of a function such as f(x) = x^2 + 2x. Thanks!

    P.S - Please dont use any big calculus words - im only in triginometry!
    The derivative of  f(x) = x^2 + 2x is not what you said it was.

    You said that you knew that  x^n differentiates to  nx^{n-1} , and that's the only rule you need to know to differentiate the function you gave.

    Because differentiation is a linear operator, you can break the function up into little parts, and differentiate them separately, and then add them back together at the end.

    So first of all, find the derivative of  x^2 , which you know to be  2x , then find the derivative of  2x . Now, you can do that using the same rule because  x = x^1 . So the derivative of 2x is simply  2 \times (1 \times x ^{1 -1 }) = 2 \times x^0 = 2 \times 1 = 2

    So to conclude, the derivative of  x^2 is  2x , and the derivative of  2x is  2 , therefore, the derivative of  x^2 + 2x is  2x + 2 .

    Doing it the 'long way', you should have this:

     \displaystyle  f'(x) =\lim_{h \to 0} \frac{f(x+h) - f(x)}{h} = \lim_{h \to 0} \frac{(x+h)^2 + 2(x+h) - x^2 - 2x}{h}

     = \lim_{h \to 0} \frac{x^2 + 2xh + h^2 + 2x +2h - x^2 - 2x }{h} =  \lim_{h \to 0} \frac{ 2xh+ h^2+2h  }{h}

     =  \lim_{h \to 0} 2x +h+2 = 2x + 2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie gs.sh11's Avatar
    Joined
    Oct 2009
    Posts
    14
    Thankyou very much!! I understand this now!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contuous weak derivative $\Rightarrow$ classic derivative ?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 22nd 2011, 02:37 AM
  2. Replies: 0
    Last Post: January 24th 2011, 11:40 AM
  3. [SOLVED] Definition of Derivative/Alt. form of the derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 23rd 2010, 06:33 AM
  4. Derivative Increasing ==> Derivative Continuous
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 23rd 2010, 10:58 AM
  5. Replies: 2
    Last Post: November 6th 2009, 02:51 PM

Search Tags


/mathhelpforum @mathhelpforum