Differentiate `(e^xsinx)/((x^2+2)^3)` with respect to `x` .

Explanation

To differentiate the function \( y = \frac{e^x \sin x}{(x^2 + 2)^3} \) with respect to \( x \), we will use the quotient rule. The quotient rule states that if you have a function \( y = \frac{u}{v} \), then the derivative \( \frac{dy}{dx} \) is given by:

\[ \frac{dy}{dx} = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2} \]

where \( u = e^x \sin x \) and \( v = (x^2 + 2)^3 \).

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