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    Hi, I have many questions about implicit differentiation (which we didn't learn how to do in class I guess):

    1. Given that x = cos(y), find dy/dx in terms of x, using the fact y = cos^-1x

    2. Given that x = tan(y), find dy/dx in terms of x, using the fact y = tan^-1x

    3. Given y = x^x^2, find dy/dx in terms of x.

    4. Find dy/dx in terms of x and y for the equation: e^xy = 2 (answer is = y/x, but I'm getting -e^x/e^y)

    For Q1-2 I can find dy/dx in terms of x and y, but I find dy/dx in terms of x by using the facts.

    Thanks in advance.
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    (Original post by TheKevinFang)
    Hi, I have many questions about implicit differentiation (which we didn't learn how to do in class I guess):

    1. Given that x = cos(y), find dy/dx in terms of x, using the fact y = cos^-1x

    2. Given that x = tan(y), find dy/dx in terms of x, using the fact y = tan^-1x

    3. Given y = x^x^2, find dy/dx in terms of x.

    4. Find dy/dx in terms of x and y for the equation: e^xy = 2 (answer is = y/x, but I'm getting -e^x/e^y)

    For Q1-2 I can find dy/dx in terms of x and y, but I find dy/dx in terms of x by using the facts.

    Thanks in advance.
    This belongs in the Maths forum I've asked for this thread to be moved there. :borat:

    It's not quite clear what you mean for Q1/2 - please post working if possible.

    What have you tried for Q3/4? (You've got an answer for 4 but we can't see where you're going wrong or why).
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    Moved to maths.
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    (Original post by TheKevinFang)
    Hi, I have many questions about implicit differentiation (which we didn't learn how to do in class I guess):

    1. Given that x = cos(y), find dy/dx in terms of x, using the fact y = cos^-1x

    2. Given that x = tan(y), find dy/dx in terms of x, using the fact y = tan^-1x

    3. Given y = x^x^2, find dy/dx in terms of x.

    4. Find dy/dx in terms of x and y for the equation: e^xy = 2 (answer is = y/x, but I'm getting -e^x/e^y)

    For Q1-2 I can find dy/dx in terms of x and y, but I find dy/dx in terms of x by using the facts.

    Thanks in advance.
    Ill do Q1 for you and see if you spot how I'm doing it, I can explain if needed. Then you can try the rest

    x = cosy

    \dfrac{dx}{dy} = -siny

    \therefore \dfrac{dy}{dx} = -\dfrac{1}{siny}

    It is given that x=cosy and we know that cos^{2}y+sin^{2}y=1

     sin^{2}y = 1-cos^{2}y

    \therefore siny = \sqrt{1-cos^{2}y}

    siny = \sqrt{1-x^{2}} (as x=cosy)

    \therefore \dfrac{dy}{dx} = -\dfrac{1}{\sqrt{1-x^{2}}}
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    Since when is differentiation of inverse trigonometric functions in c4?


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    (Original post by drandy76)
    Since when is differentiation of inverse trigonometric functions in c4?


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    It's not
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    Using implicit differentiation :
    X=cosy
    1=-siny dy/dx
    Dy/dx = -1/siny
    Siny =(1-cos^2x)^1/2
    X^2=cos^2x
    Dy/dx =-1/(1-x^2)^1/2


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    For question 4 you should get (Y+xdy/dx)e^xy=0 then simplify from there




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    (Original post by edothero)
    It's not
    Honestly thought it was MEI being weird with their spec again


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