Find the derivative of $f(x) = \sqrt{2x + 3}$ from first principles (definition of derivative).

Find the derivative of $f(x) = \sin(3x)$ from first principles.

Find from first principles (definition of derivative) the derivative of $f(x) = x^n$ where $n$ is any positive integer.

Find $\frac{dy}{dx}$ and $\frac{d^2y}{dx^2}$ for the cycloid defined parametrically by: $$x = a(\theta - \sin\theta), \quad y = a(1 - \cos\theta)$$ Evaluate both at $\theta = \frac{\pi}{2}$.