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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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
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$\frac{-4\frac{d}{dn}\left(-5m^5n^2-\frac{1}{2}m^4n^4+\frac{2}{3}m^3n-4mn^4\right)m^5n^3-\left(-5m^5n^2-\frac{1}{2}m^4n^4+\frac{2}{3}m^3n-4mn^4\right)\frac{d}{dn}\left(-4m^5n^3\right)}{\left(-4m^5n^3\right)^2}$
Learn how to solve problems step by step online. Find the derivative of (-5m^5n^2-1/2m^4n^42/3m^3n-4mn^4)/(-4m^5n^3). 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. Simplify the product -(-5m^5n^2-\frac{1}{2}m^4n^4+\frac{2}{3}m^3n-4mn^4). Simplify the product -(-\frac{1}{2}m^4n^4+\frac{2}{3}m^3n-4mn^4).