if `y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/(sqrt(a-x)+sqrt(x-b))` then `dy/dx` wherever it is defined is equal to`:`

Options

A. `(x+(a+b))/(sqrt((a-x)(x-b)))`
B. `(2x-a-b)/(2sqrt(a-x)sqrt(x-b))`
C. `-((a+b))/(2sqrt((a-x)(x-b)))`
D. `(2x+(a+b))/(2sqrt((a-x)(x-b)))`

Explanation

To find the derivative \( \frac{dy}{dx} \) of the function

\[ y = \frac{(a-x)\sqrt{a-x} - (b-x)\sqrt{x-b}}{\sqrt{a-x} + \sqrt{x-b}}, \]

we will follow these steps:

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