Can someone answer : find dy/dx by implicit differentation, if y cos x = x sin y?

implicit
differentation

#1

can someone answer : find dy/dx by implicit differentation, if y cos x = x sin y?

Answer:

Use product rule and implicit differentiation,
product rule d/dx(uv) = u’v + v’u.
Hence your answer is given by,

dy/dxcos(x) -ysin(x) = sin(y) + xdy/dxsin(y) .

dy/dx*(cos(x) -xsin(y)) = sin(y)(1-y)

dy/dx= (cos(x) - xsin(y))/(sin(y)(1-y)).