Mathematics

The domain of $h'(x)$ is narrower than the domain of $h(x)$ itself—you need to find where $h$ is actually differentiable, not just defined. Start by identifying where $h(x)$ exists (the square root and denominator constraints), then check where the derivative fails to exist. The key is recognizing that $\sqrt{x-1}$ has a vertical tangent at its endpoint, making the derivative undefined there even though the function is defined.

The domain of $h'(x)$ is narrower than the domain of $h(x)$ itself—you need to find where $h$ is actually differentiable, not just defined. Start by identifying where $h(x)$ exists (the square root and denominator constraints), then check where the derivative fails to exist. The key is recognizing that $\sqrt{x-1}$ has a vertical tangent at its endpoint, making the derivative undefined there even though the function is defined.