Question

find dy/dx for cosxy-cos^2y=k​

Answer 1

Answer:

(y sin xy) / [ sin2y - x sin xy]

explanation:

given: cos xy - cos²y = k

differentiate w.r.t X,

d(cosxy)/dx - d(cos² y)/dx = d(k)/dx

-sin xy *(d(xy)/dx) -(-2 siny cosy Dy/dx) = 0

-sin xy ( y+ x Dy/dx) + (sin2y * Dy/dx) =0

-y sin xy - x sin xy * Dy/dx + sin 2y Dy/dx =0

Dy/dx [ sin2y - x sin xy] = y sin xy

Dy/dx = (y sin xy) / [ sin2y - x sin xy]