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    How does one implicitly differentiate \sqrt {(xy)} ?

    Apart from changing the surd form into a power, I don't know how to progress from here.

    The full question is \sqrt {(xy)} + x + y^2 = 0 for those who may ask but I already know how to differentiate x and y^2

    Help is always appreciated
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    To implicitly differentiate this you have to differentiate each term with respect to X and use the product rule. This would give (0.5X^-0.5)(Y^0.5) + (X^0.5)(0.5Y^-0.5)dy/dx
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    (Original post by ManLike007)
    How does one implicitly differentiate \sqrt {(xy)} ?

    Apart from changing the surd form into a power, I don't know how to progress from here.

    The full question is \sqrt {(xy)} + x + y^2 = 0 for those who may ask but I already know how to differentiate x and y^2

    Help is always appreciated
    Let a=\sqrt{xy} and let u=xy.

    What is \displaystyle \frac{da}{du}?

    What is \displaystyle \frac{du}{dx}?

    Then \displaystyle \frac{da}{dx}=\frac{da}{du}\cdot \frac{du}{dx}

    Slightly alternative approach:

    Spoiler:
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    a^2=xy then differentiate a^2 and xy wrt to x and rearrange for y' before back-substituing for a



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    Ahh okay I get it now, thanks for your time!
 
 
 
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