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    Find dy/dx as a fuction of x if y^2 = 2x +1

    I don't really understand what to do here. What does it mean 'as a function of x'? Does it mean I can't have y's in my answer? Pls help!
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    You need to have it in the form \frac{dy}{dx} = f(x)
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    Differentiate both sides with respect to x.  \frac{d}{dx} (y^2)=\frac{dy}{dx} \cdot \frac{d}{dy} (y^2) .
    As for the meaning of a function of x, it means you need it in the form  \frac{dy}{dx} = f(x) rather than  \frac{dy}{dx} = f(x, y) , basically meaning you don't want any y terms in your expression do dy/dx.
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    (Original post by NotNotBatman)
    You need to have it in the form \frac{dy}{dx} = f(x)
    So after I differentiate it, I'll need to get rid of the y's?
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    (Original post by B_9710)
    Differentiate both sides with respect to x.  \frac{d}{dx} (y^2)=\frac{dy}{dx} \cdot \frac{d}{dy} (y^2) .
    As for the meaning of a function of x, it means you need it in the form  \frac{dy}{dx} = f(x) rather than  \frac{dy}{dx} = f(x, y) .
    Ahh thank you so much!
    For the second derivative, will I need to have the answer in the dy/dx = f(x) form before differentiating again?
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    (Original post by IDontKnowReally)
    So after I differentiate it, I'll need to get rid of the y's?
    Yes.

    (Original post by IDontKnowReally)
    Ahh thank you so much!
    For the second derivative, will I need to have the answer in the dy/dx = f(x) form before differentiating again?
    No, but it would be in that form anyway.
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    (Original post by NotNotBatman)
    Yes.



    No, but it would be in that form anyway.
    How?
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    (Original post by IDontKnowReally)
    How?
    Just differentiate and rearrange for \frac{dy}{dx} =f(x). and use  y^2= 2x+1 to find y in terms of x.
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    (Original post by NotNotBatman)
    Just differentiate and rearrange for \frac{dy}{dx} =f(x). and use  y^2= 2x+1 to find y in terms of x.
    I understood that but just wasn't sure how it would be in that form before differentiating anyway.
    Thanks for all your help!
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    (Original post by IDontKnowReally)
    I understood that but just wasn't sure how it would be in that form before differentiating anyway.
    Thanks for all your help!
    Are you given any restrictions on the domain of y? Because if you're not, you CAN'T write y as a function of x as it stands - there are two possible choices available when you try to take the square root!
 
 
 
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