Polymyositis and Dermatomyositis
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Differentiate both sides: d/dx(x²y³) = d/dx(ln y) ⇒ 2xy³ + x²·3y² dy/dx = (1/y) dy/dx. Collect dy/dx terms: dy/dx (3x²y² - 1/y) = -2xy³. Multiply by y: dy/dx (3x²y³ - 1) = -2xy⁴. Thus dy/dx = (-2xy⁴)/(3x²y³ - 1).
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