Calculus: Early Transcendentals, Chapter 3, 3.5, Section 3.5, Problem 28

Note:- 1) If y = x^n ; then dy/dx = n*x^(n-1) ; where n = real number
2) If y = u*v ; where both u & v are functions of 'x' , then
dy/dx = u*(dv/dx) + v*(du/dx)
3) If y = k ; where 'k' = constant ; then dy/dx = 0
Now, the given function is :-
(x^2) + 2xy - (y^2) + x = 2
Differentiating both sides w.r.t 'x' we get;
2x + 2x(dy/dx) + 2y - 2y(dy/dx) + 1 = 0
Putting x =1 & y =2 in the above equation we get
slope of the tangent at (1,2) = dy/dx at (1,2) = 7/2
Now, equation of the tangent to the given curve at (1,2) is :-
y - 2 = (7/2)*(x-1)
or, 2y - 4 = 7x - 7
or, 2y = 7x - 3 = equation of the tangent at point (1,2)