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