Asked by Kim

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...

Answers

Answered by drwls
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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