Posted by DJ on .
(y/(x+9y))= (x^2)7
at the point (1, 6/55)
Use implicit differentiation to find the slope of the tangent line to the curve

Calculus 
Reiny,
crossmultiply first
y = x^3  7x + 9x^2y  63y
y' = 3x^2  7 + 9x^2y' + 18xy  63y' , where y' = dy/dx
64y'  9x^2y' = 3x^2 + 18xy7
y' = dy/dx = (3x^2 + 18xy  7)/(64  9x^2)
I will leave it up to you to do the remaining arithmetic