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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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$\frac{\frac{d}{dx}\left(4x^2+12yx+9y^2\right)\left(3y+2x\right)-\left(4x^2+12yx+9y^2\right)\frac{d}{dx}\left(3y+2x\right)}{\left(3y+2x\right)^2}$
Learn how to solve problems step by step online. Find the derivative using the quotient rule (4x^2+12yx9y^2)/(3y+2x). 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+12yx+9y^2). Simplify the product -(12yx+9y^2). The derivative of a sum of two or more functions is the sum of the derivatives of each function.