Results 1 to 4 of 4

Math Help - Implicit Differentiation

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    36

    Implicit Differentiation

    First time using LaTeX. Found it to be quick and easy on the eyes.

    1) If cos x = e^y and x is greater than zero and less than pi, what is dy/dx in terms of x.


    my steps
    -take the derivative of both sides -sinx=e^y (dy/dx)

    -this is where i am lost. I think I should take the ln of each side but i am not sure. All help is appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Feb 2009
    From
    Posts
    79
    Quote Originally Posted by dandaman View Post
    First time using LaTeX. Found it to be quick and easy on the eyes.

    1) If cos x = e^y and x is greater than zero and less than pi, what is dy/dx in terms of x.


    my steps
    -take the derivative of both sides -sinx=e^y (dy/dx)

    -this is where i am lost. I think I should take the ln of each side but i am not sure. All help is appreciated.
    cos x = e^y

    Differentiate both sides

    (cosx) ' = (e^y)'

    (cosx) ' = -sinx *(x)' = -sinx -- chain rule

    (e^y)'= e^y * y' -- chain rules

    -sinx = (e^y) y'

    y' = -sinx /(e^y)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by dandaman View Post
    First time using LaTeX. Found it to be quick and easy on the eyes.

    1) If cos x = e^y and x is greater than zero and less than pi, what is dy/dx in terms of x.


    my steps
    -take the derivative of both sides -sinx=e^y (dy/dx)

    -this is where i am lost. I think I should take the ln of each side but i am not sure. All help is appreciated.
    Note that your work leads to \frac{\,dy}{\,dx}=-\frac{\sin x}{e^y}

    But what did we say e^y originally was? (That's my BIG hint)

    Can you take it from here?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jan 2009
    Posts
    36
    OHHHHH... Thanks a ton you two... That was a good hint also... Thanks thanks thanks
    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. implicit differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 1st 2010, 08:42 AM
  3. Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 28th 2010, 04:19 PM
  4. Implicit differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 26th 2010, 06:41 PM
  5. Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 25th 2008, 08:33 PM

Search Tags


/mathhelpforum @mathhelpforum