use implicit differentiation to find the slope of the tangent line to the curve (y)/(x-7y)=x^6+5 at the point (1,6/43)

Answer 1

I would cross-multiply, then simplify to avoid using the quotient rule to get

36y = x^7 + 5x - 7x^6y
36dy/dx = 7x^6 + 5 -7x^6dy/dx - y(42x^5)
dy/dx(36 + 7x^6) = 7x^6 + 5x - 42yx^5
dy/dx = (7x^6 + 5x - 42yx^5)/(36+7x^6)

sub in x=1 and y = 6/43)

I will leave the arithmetic for you

Answer 2

THANK YOU !

Answer 3

when you cross multiply how do you get 36y?