Find dy/dx when y=0 if xcos(y)-sin(x)-2=0?

Answer 1

xcos(y) --> For this part, use the product rule, which would mean
cosy - xsiny * dy/dx

sinx's derivative is just cosx, so we get as a final answer

cosy - xsiny * dy/dx - cosx =0
-xsiny *dy/dx = cosx - cosy
dy/dx = cosx - cosy / -xsiny

When y=0,
dy/dx = cosx - cosy / -xsiny
dy/dx = cosx - cos(0) / -xsin(0) [note: sin(0) =0]
dy/dx = undefined [since you can't divide by 0]

Answer 2

x cos y - sin x - 2 = 0
cos y - sin y (dy/dx)(x) - cos x = 0
- x sin y (dy/dx) = cos x - cos y
x sin y (dy/dx) = cos y - cos x
dy/dx = (cos y - cos x) / (x sin y)
This leads to a problem in that denominator = 0 when y = 0?

Answer 3

I think it's zero
dy/dx = [dy/dt]/[dx/dt] = [-xsin(y)]/[cos(y)-cos(x)]
y=0 then 0/[1-cos(x)] = 0