Question

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

Answer 1

Step 1:

The curve equation is and the tangent point is .

The slope of the tangent line is equal to the derivative of the function at .

.

Apply derivative on each side with respect to x.

Apply derivative rule of constants .

Apply inverse trigonometric derivative rule .

Step 2:

The slope of the tangent line is .

Substitute for in the above equation.

This is the Slope of the tangent line is at .

Step 3:

The point-slope form of line equation is .

Find the tangent line equation by substituting values of and in the above equation.

The equation of the tangent line is .

Solution:

The equation of the tangent line is .