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Thread: Implicit Differentiation

  1. #1
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    Implicit Differentiation

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

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


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

    -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.
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  2. #2
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    Quote Originally Posted by dandaman View Post
    First time using LaTeX. Found it to be quick and easy on the eyes.

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


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

    -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.
    $\displaystyle 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)
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by dandaman View Post
    First time using LaTeX. Found it to be quick and easy on the eyes.

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


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

    -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 $\displaystyle \frac{\,dy}{\,dx}=-\frac{\sin x}{e^y}$

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

    Can you take it from here?
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  4. #4
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    OHHHHH... Thanks a ton you two... That was a good hint also... Thanks thanks thanks
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