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Math Help - help me with finding equation of tangent (implicit differentiation)

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    help me with finding equation of tangent (implicit differentiation)

    please someone help me with this:
    Consider the curve
    The equation of the tangent line to the curve at the point has the form where
    _________and _________________
    Last edited by mr fantastic; October 17th 2009 at 06:35 PM. Reason: Re-named post to a less deceptive name.
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    Quote Originally Posted by zpwnchen View Post
    please someone help me with this:

    Consider the curve
    The equation of the tangent line to the curve at the point has the form where
    _________and _________________
    Differentiate implicitly:

    6x^5+2x\frac{dy}{dx}+2y+4y^3\frac{dy}{dx}=0 \implies \frac{dy}{dx}=-\frac{6x^5+2y}{2x+4y^3}

    Plug in (1,1) to find the slope and then use the point-slope equation to find the tangent line.
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    Why do i have to use implicit differentiation?
    <br />
m = f_{x} (x,y) so F_x = 6x^5+2y = 6+2 =8.. why is not right?
    Last edited by zpwnchen; October 17th 2009 at 07:40 PM.
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    Quote Originally Posted by zpwnchen View Post
    Why do i have to use implicit differentiation?
    <br />
m = f_(x) (x,y) so F_x = 6x^5+2y = 6+2 =8.. why is not right?
    .
    This is wrong. You require the value of dy/dx at the given point. Note that y is an implicit function of x.
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    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by zpwnchen View Post
    Why do i have to use implicit differentiation?
    <br />
m = f_(x) (x,y) so F_x = 6x^5+2y = 6+2 =8.. why is not right?
    This is not a function of three variables (i.e. z=f(x,y)) and therefore partial derivatives are not necessary because you are only trying to find \frac{dy}{dx}.
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    Quote Originally Posted by zpwnchen View Post
    Why do i have to use implicit differentiation?
    <br />
m = f_{x} (x,y) so F_x = 6x^5+2y = 6+2 =8.. why is not right?
    So this is right when y is not included in the function?
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    Please delete it
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    Quote Originally Posted by zpwnchen View Post
    So this is right when y is not included in the function?
    Right for what? This makes no sense.

    You are clearly confusing functions of several variables with functions of a single variable. To get the tangent to a curve defined by the relation f(x, y) = c you need to calculate dy/dx. To do this you either make y the subject (where possble or convenient) and differentiate or you just differentiate the relation using implicit differentiation and then solve for dy/dx. Either way, f(x, y) = c defines a function of a single variable.
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    i mean. if it's f(x) function(single variable) then i do not need to implicitly differentiate and just F_{x} would give me m right?
    Because it is a f(x y) function (several variable) so i have to implicit differentiate dy/dx to get m right?
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  10. #10
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by zpwnchen View Post
    i mean. if it's f(x) function(single variable) then i do not need to implicitly differentiate and just F_{x} would give me m right?
    Because it is a f(x y) function (several variable) so i have to implicit differentiate dy/dx to get m right?
    You could think of the function as x^6+2xf(x)+f^4(x)=4.

    That, you can see, is a function of one variable. If you could solve for f(x), than you could just take a regular derivative, but since solving for f(x) is either very hard or impossible, it makes the most sense to differentiate implicitly.
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