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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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$\frac{\frac{d}{dx}\left(-x^4-22x^3+134x^2+280x-996\right)\left(x^5-3x^4-23x^3+51x^2+94x-120\right)-\left(-x^4-22x^3+134x^2+280x-996\right)\frac{d}{dx}\left(x^5-3x^4-23x^3+51x^2+94x-120\right)}{\left(x^5-3x^4-23x^3+51x^2+94x-120\right)^2}$
Learn how to solve problems step by step online. Find the derivative of (-x^4-22x^3134x^2280x+-996)/(x^5-3x^4-23x^351x^294x+-120). 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^4-22x^3+134x^2+280x-996). Simplify the product -(-22x^3+134x^2+280x-996). Simplify the product -(134x^2+280x-996).