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$\frac{d}{dx}\left(\frac{\left(x^{-4}y\right)^{-\frac{1}{2}}}{\left(x^2y^3\right)^{-\frac{1}{3}}}\right)$
Learn how to solve differential equations problems step by step online. Find the derivative using the quotient rule ((x^(-4)y)^(-1/2))/((x^2y^3)^(-1/3)). Simplifying. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. The power of a product is equal to the product of it's factors raised to the same power. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}.