Results 1 to 5 of 5

Math Help - def. of deriv

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    56

    def. of deriv

    Use the definition of derivative to find d/dx cos(x).

    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by kwivo View Post
    Use the definition of derivative to find d/dx cos(x).
    by the limit definition of the derivative:

    \frac d{dx}f(x) = \lim_{h \to 0} \frac {f(x + h) - f(x)}h

    thus, \frac d{dx} \cos(x) = \lim_{h \to 0}\frac {\cos (x + h) - \cos x }h

    now, continue (begin by using the addition formula for cosine to expand \cos (x + h) in the numerator
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    You can use the addtion formula for cos.

    \frac{d}{dx}[cos(x)]=\lim_{h\rightarrow{0}}\frac{cos(x+h)-cos(x)}{h}

    = \lim_{h\rightarrow{0}}\frac{cos(x)cos(h)-sin(x)sin(h)-cos(x)}{h}

    = \lim_{h\rightarrow{0}}\left[cos(x)\left(\frac{cos(h)-1}{h}\right)-sin(x)\left(\frac{sin(h)}{h}\right)\right]

    Can you finish?.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2007
    Posts
    56
    Ok, I'm not sure how to get rid of the cos(h)-1/h, but the sin(h)/h is equal to 1 right?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by kwivo View Post
    Ok, I'm not sure how to get rid of the cos(h)-1/h, but the sin(h)/h is equal to 1 right?
    \lim_{x \to 0} \frac {\cos x - 1}x happens to be a special limit. look it up. ... nevermind, it's equal to zero.

    yes, \lim_{h \to 0} \frac {\sin h}h = 1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Partial Deriv. Help
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 14th 2009, 04:27 PM
  2. Deriv
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 29th 2008, 01:16 AM
  3. deriv again
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 11th 2007, 04:11 PM
  4. log deriv.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 11th 2007, 08:40 AM
  5. deriv. of ln
    Posted in the Calculus Forum
    Replies: 6
    Last Post: October 8th 2007, 10:45 PM

Search Tags


/mathhelpforum @mathhelpforum