Final Answer
Step-by-step Solution
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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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$\frac{\frac{d}{dx}\left(9x^3-4x^2+30x-10\right)\left(x-1\right)-\left(9x^3-4x^2+30x-10\right)\frac{d}{dx}\left(x-1\right)}{\left(x-1\right)^2}$
Learn how to solve integral calculus problems step by step online. Find the derivative of (9x^3-4x^230x+-10)/(x-1). 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 -(9x^3-4x^2+30x-10). Simplify the product -(-4x^2+30x-10). Simplify the product -(30x-10).