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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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$\frac{\frac{d}{dx}\left(xe^{\left(2x-6\right)}-7x+18\right)\left(x^3-5x^2+3x+9\right)-\left(xe^{\left(2x-6\right)}-7x+18\right)\frac{d}{dx}\left(x^3-5x^2+3x+9\right)}{\left(x^3-5x^2+3x+9\right)^2}$
Learn how to solve differential calculus problems step by step online. Find the derivative of (xe^(2x-6)-7x+18)/(x^3-5x^23x+9). 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 -(xe^{\left(2x-6\right)}-7x+18). Simplify the product -(-7x+18). The derivative of a sum of two or more functions is the sum of the derivatives of each function.