Find an equation of the tangent line to the curve y = sin (sin (x)) at the point (2pi, 0)?

Answer 1

dy/dx = cos(sin(x))cos(x) at x = 2*pi, dy/dx = 1 So the tangent line is

y-o =(1)(x - 2*pi) or y = x - 6.283

Answer 2

y=sin(sinx) dy/dx = cos(sinx)cosx at (2π,0) dy/dx =cos(sin2π)cos2π =cos(0)•1=1 so the slope of the tangent line is 1. Using the equation for a straight line y=mx +b then at (2π,0) 0=1•2π +b and b= -2π. So the equation of the tangent line is y= x - 2π