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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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$\frac{\frac{d}{dx}\left(\left(x+3\right)^2\left(2x+3\right)\right)\left(x-3\right)\left(1-5x\right)-\left(x+3\right)^2\left(2x+3\right)\frac{d}{dx}\left(\left(x-3\right)\left(1-5x\right)\right)}{\left(\left(x-3\right)\left(1-5x\right)\right)^2}$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(((x+3)^2(2x+3))/((x-3)(1-5x))). 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}}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The power of a product is equal to the product of it's factors raised to the same power. Simplify the product -(2x+3).