,

Differentiate both sides of the equation.

The derivative of with respect to is .

Differentiate the right side of the equation.

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

The derivative of with respect to is .

Reorder the factors of .

Reform the equation by setting the left side equal to the right side.

Replace with .

Evaluate at and .

Replace the variable with in the expression.

Subtract full rotations of until the angle is greater than or equal to and less than .

The exact value of is .

Multiply by .

Subtract full rotations of until the angle is greater than or equal to and less than .

The exact value of is .

The exact value of is .

Plug in the slope of the tangent line and the and values of the point into the point–slope formula .

The slope-intercept form is , where is the slope and is the y-intercept.

Rewrite in slope-intercept form.

Subtract from .

Simplify .

Multiply by .

Multiply by .

Find the Tangent Line at the Point y=sin(sin(x)) , (4pi,0)