Find y” by implicit differentiation.

Question

find y” by implicit differentiation cos(y) + sin(x) = 1

Answer 1

cosy + sinx = 1

-siny(dy/dx) + cosx = 0

dy/dx = cosx / siny

d²y/dx² = [sinycosx(-sinx) - cosxcosy(dy/dx] / sin²y

= [-sinxcosxsiny - cosxcosy(cosx/siny)] / sin²y

= [-sinxcosxcosy - cos²xcoty] / sin²y