Question

find the derivatives of the function y= xsinx/x+sinx​

Answer 1

Step-by-step explanation:

$y = \frac{x \sin \: x}{x + \sin \: x } \\ \frac{dy}{dx} = \frac{(x + \sin \: x) \frac{d}{dx} (x \sin \: x) -(x \sin \: x ) \frac{d}{dx}(x + \sin \: x) }{(x + \sin \: x)^{2} } \\ = \frac{(x + \sin \: x)(x \cos \: x + \sin \: x) - (x \sin \: x)(1 + \cos \: x) }{(x + \sin \: x)^{2}} \\ = \frac{ {x}^{2} \cos \: x + x \sin \: x + x \sin \: x \cos \: x + { \sin }^{2} x - x \sin \: x - x \sin \: x \cos \: x }{(x + \sin \: x)^{2}} \\ = \frac{ {x}^{2} \cos \: x + { \sin}^{2}x }{(x + \sin \: x)^{2}}$