Let x = secθ - cosθ and y = sec⁴θ - cos⁴θ. What is (dy/dx)² equal to?

Let u = sec²θ + cos²θ. Then x² = sec²θ - 2 + cos²θ = u - 2, so u = x²+2. y = sec⁴θ - cos⁴θ = (sec²θ-cos²θ)(sec²θ+cos²θ). Also sec²θ - cos²θ = (secθ-cosθ)(secθ+cosθ). And y² = (sec⁴θ-cos⁴θ)² ... Using y = x·(secθ+cosθ)·u where (secθ+cosθ)² = sec²θ + 2 + cos²θ = u+2 = x²+4. So y² = x²(x²+4)u² and also y² + 4·(secθ·cosθ)⁴... Standard result: (dy/dx)² = 16(y²+4)/(x²+4).