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Math Help - Implicit Differentiation Slope Tangent Line

  1. #1
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    Implicit Differentiation Slope Tangent Line

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

    y/(x-3y) = x^6 + 8 at the point (1, 9/28)

    m = ?

    i tried using quotient rule but cannot seem to get the correct answer. this is what i have done

    [(dy/dx)(x-3y)-(1-3dy/dx)(y)]/(x-3y)^2 = 6x^5

    --> [x(dy/dx)]/(x-3y)^2 = 6x^5 + y

    dy/dx = [(6x^5 + y)(x-3y)^2]/x
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  2. #2
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    \frac{y}{x-3y} = x^6 + 8

    y = x^7 + 8x - 3x^6y - 24y

    25y = x^7 + 8x - 3x^6y

    25\frac{dy}{dx} = 7x^6 + 8 - 3x^6 \frac{dy}{dx} - 18x^5y

    \frac{dy}{dx} = \frac{7x^6 + 8 - 18x^5y}{3x^6 + 25}

    see if that works.
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  3. #3
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    it did work thanks a lot
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