Assume, 
Upon differentiating with respect to 
![{f^\prime }(x) = \cos \frac{\pi }{4} \cdot \left[ {\frac{{\sin x\frac{d}{{dx}}\left( {{x^2}} \right) - {x^2}\frac{d}{{dx}}(\sin x)}}{{{{\sin }^2}x}}} \right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c0422d349263a3644f089fc33472e8d9_l3.png "Rendered by QuickLaTeX.com")
![f'(x) = \cos \frac{\pi }{4} \cdot \left[ {\frac{{\sin x \cdot 2x - {x^2}\cos x}}{{{{\sin }^2}x}}} \right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d06e0ff26d64481263c25ada81e7f75f_l3.png "Rendered by QuickLaTeX.com")
Therefore, ![f'(x) = \frac{{x\cos \frac{\pi }{4}[2\sin x - x\cos x]}}{{{{\sin }^2}x}}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9ed131274e2f0ee65795b50bd0a7ff99_l3.png "Rendered by QuickLaTeX.com")
Find the derivative of the following functions (it is to be understood that 
