Question

Use implicit differentiation to find the slope of the tangent line to the curve xy^3+xy=10 at the point (5,1)

Answer 1

I already did the implicit differentiation and got \[\frac{ -y^3+y }{ 3xy^2+x }\]

Answer 2

check the minus sign on the top of the fraction

Answer 3

Should it be positive?

Answer 4

\[\dfrac{dy}{dx} = -\dfrac{ y^3+y }{ 3xy^2+x }\]

Answer 5

Okay gotcha, I'm just not sure where to go from here

Answer 6

plug in x and y

??

Answer 7

ohh okay i using my original equation which was giving me the wrong answer but I got it now! Thanks!!

Answer 8

try out the Implicit Function Theorem:

\(\dfrac{dy}{dx} = -\dfrac{f_x}{f_y}\) :-))