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$\frac{d}{dx}\left(\frac{x^{\left(3y+2\right)}}{x^{\left(4y-2\right)}}\right)$
Learn how to solve problems step by step online. Find the derivative using the quotient rule (x^(2y-3)x^(y+5))/(x^(3y+1)x^(y-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}}. The derivative \frac{d}{dx}\left(x^{\left(3y+2\right)}\right) results in \frac{\left(3x^{\left(3y+2\right)}+2\right)x^{\left(3y+1\right)}}{1-3x^{\left(3y+2\right)}\ln\left(x\right)}. The derivative \frac{d}{dx}\left(x^{\left(4y-2\right)}\right) results in \frac{2\left(2x^{\left(4y-2\right)}-1\right)x^{\left(4y-3\right)}}{1-4x^{\left(4y-2\right)}\ln\left(x\right)}.