Mathematics

The key is recognizing that you're not finding $\frac{dy}{dx}$, but rather $\frac{dy}{du}$ where $u = \sqrt{1-x^2}$ is your new variable. Use the chain rule to connect the derivative of the inverse secant function to the rate of change of $u$: $\frac{dy}{du} = \frac{dy/dx}{du/dx}$. Then substitute $x = \frac{1}{2}$ to evaluate at that specific point.

The key is recognizing that you're not finding $\frac{dy}{dx}$, but rather $\frac{dy}{du}$ where $u = \sqrt{1-x^2}$ is your new variable. Use the chain rule to connect the derivative of the inverse secant function to the rate of change of $u$: $\frac{dy}{du} = \frac{dy/dx}{du/dx}$. Then substitute $x = \frac{1}{2}$ to evaluate at that specific point.