If ⁴√y = x + √(x² + 4), then what is √(x² + 4) · dy/dx equal to?

Let ⁴√y = y^(1/4) = x + √(x²+4). Differentiating both sides: (1/4)y^(-3/4) · dy/dx = 1 + x/√(x²+4) = [√(x²+4) + x]/√(x²+4) = y^(1/4)/√(x²+4). So dy/dx = 4y^(3/4) · y^(1/4)/√(x²+4) = 4y/√(x²+4). Therefore √(x²+4) · dy/dx = 4y.