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$\frac{d}{dx}\left(\frac{xz^{-\frac{2}{3}}}{10\sqrt{y^{3}}}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (1/5x^2y^1/2z^1/3)/((2xyz)/(y^(-1))). Simplifying. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. 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}}. The power of a product is equal to the product of it's factors raised to the same power.