Question

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

Answer 1

Hello:
Use implicit differentiation :  y sin 12x = x cos 2y
y' sin12x+12ycos12x =cos2y -2x y'sin2y
when : x = π/2  and     y =π/4 

y' sin12(π/2) +12(π/4)cos12(π/2) =cos2(π/4) -2(π/2) y'sin2(π/4)
y' sin(π/6) +(π/3)cos(π/6) =cos(π/2) -  π y'sin(π/2)


y' (1/2) +(π/3)(√3/2) = -  π 

y' (1/2) =-(π/3)(√3/2)  -  π 
y'  = -π (1+√3)/3
an equation of the tangent line is : y- π/4 = ( -π (1+√3)/3)(x-π/2)