ln(y)=2y^2-x; (2,1)

Question

Use implicit differentiation to find y prime with respect to x (dy/dx) and evaluate at the indicated point.

Answer 1

ln(y)=2y^2-x

Take derivative both sides with respect to x.

d/dx(ln(y))=(d/dx)(2y^2-x)

(1/y)(dy/dx)=4y(dy/dx)-1

(4y-(1/y))(dy/dx)=1

dy/dx  =1/[(4y-(1/y))]

(dy/dx) at (2,1) =1/[4(1)-(1/1)]

                          =1/3