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$\frac{d}{dx}\left(\frac{x^2-4x+3}{x^3-27}\right)$
Learn how to solve problems step by step online. Find the derivative using the quotient rule (x^2-(3+1)x+3)/(x^3-3^3). Simplifying. 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}}. Simplify the product -(x^2-4x+3). Simplify the product -(-4x+3).