Math (Calculus)

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Use implicit differentiation to find the slope of the tangent line to the curve

y/(x–9y)=x^6–2
at the point (1,-1/-8).

Can someone please help me?
I don't understand

  • Math (Calculus) -

    puzzled, why would your write the point as
    (1 , -1/-8) and not as simply (1 , 1/8) ?

    first expand it

    y = x^7 - 2x - 9x^6 y + 18y
    0 = x^7 - 2x - 9x^6 y + 17y
    0 = 7x^6 - 2 - 9x^6 dy/dx - 54x^5y + 17dy/dx
    dy/dx(17 - 9x^6) = 54x^5y - 7x^6
    dy/dx = (54x^5y - 7x^6))/(17 - 9x^6)

    at x = 1
    dy/dx = (54(1/8) -7)/(17 - 9)
    = (-1/4) / 8
    = -1/32

    equation of tangent:

    y + 1/8 = (-1/32)(x-1)
    y = (-1/32)x + 1/32 - 1/8
    y = (-1/32)x -3/32

    check my arithmetic

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