If x = cos y = sin(x + y) then find dy/dx. – InterviewSolution

1.

If x = cos y = sin(x + y) then find dy/dx.

Answer»

Given, x cos y = sin(x + y)

Differentiating both sides w.r.t. 'x', we get

x(-sin y).(dy/dx) + cos y = cos(x + y)[1 + (dy/dx)]

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

(dy/dx)[cos(x + y) + x sin y] = cos y - cos(x + y)

∴ dy/dx = (cos y - cos(x + y))/(cos(x + y) + x sin y)

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