Find the derivative using logarithmic differentiation method $\sqrt{\frac{x^3-y^3}{x+y}\frac{x^2+2xy+y^2}{x^2+xy+y^2}}\frac{x^2-y^2}{4}$

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$\frac{d}{dx}\left(\frac{\left(x^2-y^2\right)\sqrt{\frac{\left(x^3-y^3\right)\left(x^2+2xy+y^2\right)}{\left(x+y\right)\left(x^2+xy+y^2\right)}}}{4}\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative using logarithmic differentiation method ((x^3-y^3)/(x+y)(x^2+2xyy^2)/(x^2+xyy^2))^(1/2)(x^2-y^2)/4. Simplify the derivative by applying the properties of logarithms. To derive the function \frac{\left(x^2-y^2\right)\sqrt{\frac{\left(x^3-y^3\right)\left(x^2+2xy+y^2\right)}{\left(x+y\right)\left(x^2+xy+y^2\right)}}}{4}, use the method of logarithmic differentiation. First, assign the function to y, then take the natural logarithm of both sides of the equation. Apply natural logarithm to both sides of the equality. Apply logarithm properties to both sides of the equality.