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Differentiate w.r.t. α
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\alpha +\frac{\beta }{a}
Express \beta \times \frac{1}{a} as a single fraction.
\frac{\alpha a}{a}+\frac{\beta }{a}
To add or subtract expressions, expand them to make their denominators the same. Multiply \alpha times \frac{a}{a}.
\frac{\alpha a+\beta }{a}
Since \frac{\alpha a}{a} and \frac{\beta }{a} have the same denominator, add them by adding their numerators.