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find dy/dx of xsiny+cos2y=cosy

  • calculus -

    Use implicit differentiation.

    Differentiate both sides of the equation with respect to x, treating y as a function of x.

    x cosy dy/dx + sin y - 2 sin 2y dy/dx = -sin y dy/dx

    Now solve for dy/dx. It will be a function of both x and y.

    You could also differentiate both sides with respect to y, solve for dx/dy, and take the reciprocal of the answer. The result will look different but will still be correct.

    x cos y + sin y dx/dy - 2 sin 2y = -sin y

    dx/dy = [-siny + 2 sin2y -x cos y]/sin y
    dy/dx = sin y/[-siny + 2 sin2y -x cos y]

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