Find (dy)/(dx) if:

Here are the solutions to the problems.

6. Find $\frac{dy}{dx}$ if:

a) $y = \frac{x^2 - 1}{x^2 + 1}$

Step 1: Use the quotient rule, $\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^2}$.
Let $u = x^2 - 1$, so $u' = 2x$.
Let $v = x^2 + 1$, so $v' = 2x$.

Step 2: Substitute $u, u', v, v'$ into the quotient rule formula.

$$$$