7–14. Find the derivative the following ways:
a. Using the Product Rule (Exercises 7–10) or the Quotient Rule (Exercises 11–14). Simplify your result.
y = x² - a² / x-a, where a is a constant

Verified step by step guidance

1. Step 1: Identify the function as a quotient, where the numerator is \( x^2 - a^2 \) and the denominator is \( x - a \).
2. Step 2: Recall the Quotient Rule for derivatives, which states that if \( y = \frac{u}{v} \), then \( y' = \frac{u'v - uv'}{v^2} \).
3. Step 3: Differentiate the numerator \( u = x^2 - a^2 \) to get \( u' = 2x \), since \( a^2 \) is a constant and its derivative is zero.
4. Step 4: Differentiate the denominator \( v = x - a \) to get \( v' = 1 \), since \( a \) is a constant and its derivative is zero.
5. Step 5: Substitute \( u, u', v, \) and \( v' \) into the Quotient Rule formula to find \( y' = \frac{(2x)(x-a) - (x^2 - a^2)(1)}{(x-a)^2} \) and simplify the expression.