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

I interpret the hint as asking you to identify the function and where the derivative is taken. There are a couple of natural choices. 
If you let $f(x)=\sin^2(\pi/4+x)$, your limit expression, directly from the definition of derivative, is $f'(0)$. Now calculate $f'(x)$ using the ordinary rules of differentiation, and find $f'(0)$.
Or else let $f(x)=\sin^2 x$. Then our limit is the derivative of $f(x)$ at $x=\pi/4$. 
