Find an equation of the tangent line to the curve at the given point. Y=sin(sinx) , (2pi,0)

Question

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

y = sin(sin x),  (2π, 0)

 

Answer 1

The curve is , and the point is .

We can use implicit differentiation to find y '.

The implicit(or total) derivation of is,

Substitute the values of (x, y ) = in the above equation.

.

This is the slope (m ) of the tangent line to the implicit curve at .

To find the tangent line equation, substitute the values of m = 1 and (x, y ) = in the slope intercept form of an equation.

y = mx + b

.

Substitute m = 1 and in y = mx + b.

.

The tangent line equation is .