Final answer to the problem
$\frac{14y^{13}\left(x^2y-2\right)^2x^{7}+\left(-2x^{7}\left(x^2y-2\right)\left(2xy+x^2\right)-7\left(x^2y-2\right)^2x^{6}\right)y^{14}}{\left(x^2y-2\right)^{4}x^{14}}$
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Step-by-step Solution
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Simplifying
$\frac{d}{dx}\left(\left(\frac{x^{-5}y^4}{x^2y-2}\right)^2\left(xy^{2}\right)^3\right)$
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$\frac{d}{dx}\left(\left(\frac{x^{-5}y^4}{x^2y-2}\right)^2\left(xy^{2}\right)^3\right)$
Learn how to solve problems step by step online. Find the derivative of ((x^(-5)y^4)/(x^2y-2))^2((x^4y^(-5))/(x^3y^(-7)))^3. Simplifying. The power of a product is equal to the product of it's factors raised to the same power. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. The power of a product is equal to the product of it's factors raised to the same power.
Final answer to the problem
$\frac{14y^{13}\left(x^2y-2\right)^2x^{7}+\left(-2x^{7}\left(x^2y-2\right)\left(2xy+x^2\right)-7\left(x^2y-2\right)^2x^{6}\right)y^{14}}{\left(x^2y-2\right)^{4}x^{14}}$