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$\frac{d}{dn}\left(\frac{a^{\left(2+3n\right)}}{a^{\left(-2+4n\right)}}\right)$
Learn how to solve problems step by step online. Find the derivative of ((a^(2n-3))/(a^(3n+1))a^(n+5))/(a^(n-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}{dn}\left(a^{\left(2+3n\right)}\right) results in 3a^{\left(2+3n\right)}\ln\left(a\right). The derivative \frac{d}{dn}\left(a^{\left(-2+4n\right)}\right) results in 4a^{\left(-2+4n\right)}\ln\left(a\right).