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Learn how to solve differential calculus problems step by step online. Find the derivative of (x-2y(-4yy)/(x+y))/(x-3y(-5yy)/(x+y)). Simplifying. Combine all terms into a single fraction with x+y as common denominator. Combine all terms into a single fraction with x+y as common denominator. Simplify the fraction \frac{\frac{-4y^2+\left(x-2y\right)\left(x+y\right)}{x+y}}{\frac{-5y^2+\left(x-3y\right)\left(x+y\right)}{x+y}}.
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The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.