The following limit represents the derivative of a function $f$ at a point $a$. Evaluate the limit.
$$\lim\limits_{h \to 0 } \frac{\sin^2\left(\frac\pi 4+h \right)-\frac 1 2} h$$
The following limit represents the derivative of a function $f$ at a point $a$. Evaluate the limit.
$$\lim\limits_{h \to 0 } \frac{\sin^2\left(\frac\pi 4+h \right)-\frac 1 2} h$$