Question

$$\lim _ { x \rightarrow a } \frac { \sin x - \sin a } { \sqrt { x } - \sqrt { a } }$$

Evaluate

$\lim_{x\to a}\frac{\sin(x)-\sin(a)}{\sqrt{x}-\sqrt{a}}$

Differentiate w.r.t. a

$\frac{\mathrm{d}}{\mathrm{d}a}(\lim_{x\to a}\frac{\sin(x)-\sin(a)}{\sqrt{x}-\sqrt{a}})$