Final Answer
$\frac{y^{16}\left(17x-\frac{16}{3}y\right)}{\sqrt[3]{x^{19}}}$
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Step-by-step Solution
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Simplifying
$\frac{d}{dx}\left(\frac{\left(x^{-\frac{1}{5}}\sqrt{y^{3}}\right)^{10}}{\left(y^{-\frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}\right)$
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$\frac{d}{dx}\left(\frac{\left(x^{-\frac{1}{5}}\sqrt{y^{3}}\right)^{10}}{\left(y^{-\frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of ((x^(-1/5)y^(3/2))^10)/((y^((1*-2)/5)x^2/3)^5). Simplifying. The power of a product is equal to the product of it's factors raised to the same power. Simplify the fraction \frac{x^{-2}y^{15}}{y^{-2}\sqrt[3]{x^{10}}} by y. Simplify the fraction by x.
Final Answer
$\frac{y^{16}\left(17x-\frac{16}{3}y\right)}{\sqrt[3]{x^{19}}}$