Differentiate w.r.t. x the function `(cos^(-1)(x/2))/(sqrt(2x+7))` , `-2 < x < 2 `

Explanation

To differentiate the function \( y = \frac{\cos^{-1}(\frac{x}{2})}{\sqrt{2x + 7}} \) with respect to \( x \), we will use the quotient rule of differentiation. The quotient rule states that if you have a function in the form \( y = \frac{u}{v} \), then the derivative \( \frac{dy}{dx} \) is given by:

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

where \( u = \cos^{-1}(\frac{x}{2}) \) and \( v = \sqrt{2x + 7} \).

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