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    Can someone help me with these questions? this is from Edexcel C4 textbook ex.4B and 4c

    Find an expression in terms of x and y for dy/dx, given that square root of xy +x+y^2=0.

    Find dy/dx of y=xa^x and y=2^x/x
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    What have you done so far?
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    xy +x+y^2 = 0
    dy/dx = 1+2y = 0

    y=xa^x
    dy/dx = 1

    y=2^x/x
    y=0
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    (Original post by alex282)
    xy +x+y^2 = 0
    dy/dx = 1+2y = 0

    y=xa^x
    dy/dx = 1

    y=2^x/x
    y=0
    :facepalm:
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    For the first, apply the chain rule while also differentiating implicitly.

    For the second, I suggest logarithmic differentiation. This is when you take logs of both sides, simplify, and then differentiate the logarithms.

    For the third, I suggest writing this as (2^x)(x^-1) and applying the product rule, but this is because I hate the quotient rule. You'll also need to use logarithmic differentiation again, or you could write 2^x as e^ln(2^x) and use the chain rule.
 
 
 
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