Calculus Problem

Question

find y',y'(3) and the equation of the tangent line to the curve, x^2+(sin(2*pi*y)) = 9, at the point (3,8)

1) the derivative of x is given by y'=.....

2)the slope of the tangent line to the curve at (3,8) is given by y'(3)=....

3)the equation of the tangent line to the curve (3,8) is given by y=.....

Answer 1

Use implicit differentiation to get:

y'(x)=-x/(π cos 2πy)

Plug in (3,8) into this equation to get the slope of the tangent line.

The equation of the tangent will be y'(3) = (y-8)/(x-3)