Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

Question

tan(x+y)+sec(x-y)=2

Given Point: (pie/8,pie/8)

Answer 1

We tahe derivative: sec²(x + y)·(1 + y') + sec(x + y)tan(x + y)(1 + y') = 0;

At given point (π/8,π/8) we have sec²(π/4)(1 + y') + sec(π/4)tan(π/4)(1 + y') = 0

2(1 + y') + √2(1 + y') = 0; (2 + √2)(1 + y') = 0; 1 + y' = 0; y' = - 1.

Equation of tangent line: y - π/8 = -1(x - π/8); y = - x + π/4