Tangent lines and slopes

Question

Figure out the slope of the tangent line to the curve 2x^3+3y^3=xy at the point (0,1). Show all steps and full work, please show on paper.

Answer 1

Differentiate implicitly

6x² + 9y²(dy/dx) = x(dy/dx) + y

(9y² - x)(dy/dx) = y - 6x²

dy/dx = (y - 6x²)/(9y² - x)

at (0,1) dy/dx = 1/9

and the tangent line is 1/9 = (y-1)/x