Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

Answer 1

The tangent line to the curve can be determined by implicitly differentiating the equation of the curve. In this case, with the equation y sin 12x = x cos 2y, (π/2, π/4), the implicit differentiation is 12 y cos 12x dx + sin 12 x dy = -2x sin 2y dy + cos 2y dx; dx (12 y cos 12x  - cos 2y) = dy (-2x sin 2y - sin 12x). Hence

y' = (12 y cos 12x  - cos 2y) / (-2x sin 2y - sin 12x)