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** 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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$\frac{\frac{d}{dx}\left(y^2\right)\left(y+x^2\right)-y^2\frac{d}{dx}\left(y+x^2\right)}{\left(y+x^2\right)^2}$

Learn how to solve integral calculus problems step by step online. Find the derivative d/dx((y^2)/(y+x^2)). 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}}. The derivative of the constant function (y^2) is equal to zero. Any expression multiplied by 0 is equal to 0. x+0=x, where x is any expression.

** Final Answer

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