Alright so implicit differentiation is just not working out for me.

Use implicit differentiation to find the slope of the tangent line to the curve at point (4,1).

y / (x-2y) = x^3 + 4

Tried quotient rule to get the derivative of the left side, then got derivative of right side, and ultimately I got y + 3x^2 (x-2y)^2 / x-2y-2y

This is clearly not correct since the bottom would turn into zero if I plugged in x and y. Sigh...

1 answer

  1. It will be easier if you multiply it out and combine terms.
    9y = x^4 +4x -2x^3 y
    Differentiate both sides with respect to x implicitly, treating y as a function of x.
    9 dy/dx = 4x^3 + 4 -2x^3 dy/dx
    -6x^2 y
    dy/dx(9 + 2x^3) = 4x^3 + 4 - 6x^2 y
    dy/dx = [4x^3 -6x^2 y +4]/(9 + 2x^3)
    Plug in x=4 and y=1. You should not get a zero deniminator.

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