Posted by lan on .
use implicit differentiation to find the slope of the tangent line to the curve (y)/(x7y)=x^6+5 at the point (1,6/43)

math 
Reiny,
I would crossmultiply, 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 
math 
lan,
THANK YOU !

math 
Julie,
when you cross multiply how do you get 36y?