Question

Find the equation of the tangent line to x^(2/3)+y(2/3)=0 at the point (8,1)

Answer 1

\[\frac{2}{3}x^{\frac{2}{3}-1}+\frac{2}{3}y^{\frac{2}{3}-1}y'=0\]

Answer 2

\[\frac{2}{3}x^{\frac{-1}{3}}+\frac{2}{3}y^\frac{-1}{3}y'=0\]

Answer 3

\[x^\frac{-1}{3}+y^\frac{-1}{3}y'=0\]

Answer 4

\[y'=-\frac{x^\frac{-1}{3}}{y^\frac{-1}{3}}=-\frac{y^\frac{1}{3}}{x^\frac{1}{3}}\]