If `y=1+alpha/((1/x-alpha))+(beta//x)/((1/x-1)(1/x-beta))+(gamma//x^2)/((1/x-alpha)(1/x-beta)(1/x-gamma)),` find `(dy)/(dx)`

Explanation

To find \(\frac{dy}{dx}\) for the given function

\[ y = 1 + \frac{\alpha}{\left(\frac{1}{x} - \alpha\right)} + \frac{\frac{\beta}{x}}{\left(\frac{1}{x} - 1\right)\left(\frac{1}{x} - \beta\right)} + \frac{\frac{\gamma}{x^2}}{\left(\frac{1}{x} - \alpha\right)\left(\frac{1}{x} - \beta\right)\left(\frac{1}{x} - \gamma\right)}, \]

we will differentiate each term step by step.

...