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# Find the derivative of the following functions ( it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers ) $\large\frac{x^2 \cos \bigg( \Large\frac{\pi}{4}\bigg)}{\sin x}$

Let $f(x) = \large\frac{x^2 \cos \bigg( \Large\frac{\pi}{4}\bigg)}{\sin x}$
By quotient rule,
$f'(x) = \cos \large\frac{\pi}{4}$$, \bigg[\large\frac{\sin x \large\frac{d}{dx}(x^2)-x^2\large\frac{d}{dx}(\sin x)}{\sin^2x}\bigg] = \cos \large\frac{\pi}{4}$$, \bigg[\large\frac{\sin x.2x-x^2\cos x}{\sin ^2x}\bigg]$
$= \large\frac{x \cos \large\frac{\pi}{4}[2\sin x - x\cos x]}{\sin^2x}$