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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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$\frac{\frac{d}{dx}\left(\left(4x^2-20x+25\right)\left(9y^2+54y+81\right)\right)\left(6xy+18x-15y-45\right)-\left(4x^2-20x+25\right)\left(9y^2+54y+81\right)\frac{d}{dx}\left(6xy+18x-15y-45\right)}{\left(6xy+18x-15y-45\right)^2}$
Learn how to solve differential calculus problems step by step online. Find the derivative of ((4x^2-20x+25)(9y^2+54y+81))/(6xy+18x-15y+-45). 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 -(4x^2-20x+25). Simplify the product -(-20x+25). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=.