Question

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

Answer 1

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