Question

x*sinx / 1+sinx

plss answer fast...urgent

Answer 1

d/dx[xsinx / (1+sin x)]

= [ (1+sin x) d/dx (x sin x) - xsinx d/dx(1+sin x) ]/ [ 1+sinx]²

= {(1+sinx) [ xcosx +sinx] - [xsinx cosx]}/(1+sinx)²

= [xcosx +sinx +xsinxcosx +sin²x -xsinxcosx]/(1+sinx)²
=[xcosx +sinx +sin²x]/(1+sinx)²

here we used d/dx(u/v ) = (vdu -u dv)/v²
and d/dx (uv) = u dv +v du