Find equation of the line tangent to 4xylnyx2 at 41Solution4

Find equation of the line tangent to 4xy+lny=x^2 at (4,1)

4xy+lny=x^2

4y + 4xy\' + y\'/y = 2x

m at (4,1) = 4+16y\' + y\' = 8

y\' = m = 4/17

so, the line is

y = mx + c

y = 4/17 x + c

1 = 16/17 + c

c = 1/17

so, the line will be 17y = 4x + c

$Find equation of the line tangent to 4xy+lny=x^2 at (4,1)Solution4xy+lny=x^2 4y + 4xy\' + y\'/y = 2x m at (4,1) = 4+16y\' + y\' = 8 y\' = m = 4/17 so, the line$