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    How do you implicitly differentiate xy?
    I know the answer is y + x dx/dy and I understand where the x dx/dy comes from just not the Y? I'm not sure if any of that made sense thanks in advance


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    (Original post by amelia_2304)
    How do you implicitly differentiate xy?
    I know the answer is y + x dx/dy and I understand where the x dx/dy comes from just not the Y? I'm not sure if any of that made sense thanks in advance


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    Product rule u'v + v'u
    Differentiate x with respect to x = 1
    leave y alone 1*y = y
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    (Original post by amelia_2304)
    How do you implicitly differentiate xy?
    I know the answer is y + x dx/dy and I understand where the x dx/dy comes from just not the Y? I'm not sure if any of that made sense thanks in advance


    Posted from TSR Mobile
    with respect to x, you use the product rule.

    \frac{d}{dx}(xy) = (\frac{d}{dx}(x) \times y) + (\frac{d}{dx} (y) \times x)
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    (Original post by joostan)
    Product rule u'v + v'u
    Differentiate x with respect to x = 1
    leave y alone 1*y = y
    Using the product rule I've got to

    Y dx/dy + x dy/dx then what do I do? thanks for the help


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    (Original post by amelia_2304)
    Using the product rule I've got to

    Y dx/dy + x dy/dx then what do I do? thanks for the help


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    You're doing it wrong as you've differentiated with respect to both x and y.

    What's

    \dfrac{d}{dx}(x)
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    (Original post by amelia_2304)
    How do you implicitly differentiate xy?
    I know the answer is y + x dx/dy and I understand where the x dx/dy comes from just not the Y? I'm not sure if any of that made sense thanks in advance


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    What I would do is when differentiating xy I firstly differentiate with respect to x this means that I treat y as a constant so differentiating xdx you get one this is therefore 1y this contributes to the first part of answer. Then I differentiate with respect to y and get xdy/dx which is second part of answer. Final answer is y + xdy/dx.
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    (Original post by Indeterminate)
    You're doing it wrong as you've differentiated with respect to both x and y.

    What's

    \dfrac{d}{dx}(x)
    Can you show me step by step please? Sorry to be a pain


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    (Original post by amelia_2304)
    Can you show me step by step please? Sorry to be a pain


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    Definition:

    \dfrac{dy}{dx}

    means "the derivative of y with respect to x", and represents the gradient at any given point.

    Now, what's the gradient of x? So what do you get when you differentiate it with respect to x?

    Let me know if you want me to explain anything further.
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    (Original post by amelia_2304)
    Can you show me step by step please? Sorry to be a pain


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    Well if y=x, then dy/dx = 1 is something you should have come across when you first started looking at differentiation - think about when you differentiated constants, things like 2x and 3x, and things like x^2.

    From a geometric point of view, the derivative represents the slope of the tangent at any given point. If you have the line y=x, what is its slope at any point?
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    (Original post by Indeterminate)
    with respect to x, you use the product rule.

    \frac{d}{dx}(xy) = (\frac{d}{dx}(x) \times y) + (\frac{d}{dx} (y) \times x)
    I get it now thank you, the diagram wasn't showing at the bottom which is why I wasn't understanding what you were saying. Thank you for the help.


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