Find an equation of the tangent line at the given pointSolut

Find an equation of the tangent line at the given point.

Solution

Differentiating both sides

(7-y\')e^(7x-y) = (7y-7xy\')/y^2

At (2,14) (7-y\') e^ (14-14) = (98 - 14y\') / 196

So 98-14y\' = (7-y\')

So 13y\' = 91

So y\' = 7

So equation of tangent is y-14 = 7 (x-2)