Differentiate function w.r.t 'x',using first principal ` xcosx`

Explanation

Let `f(x) = xcosx`
`therefore f(x+h) = (x+h)cos(x+h)` ltbgt`therefore d/(dx)f(x)=underset(hto0)"lim"(x^(2//3))/h.2/3h(1-1/3.h/x+....)`
`=2/3x^(2//3)-1=2/3x^(-1/3)`
`=underset(hto)"lim"1/h[xcos(x+h)+hcosx(x+h)-xcosx]`
`=underset(hto0)"lim"1/h[x{-2sin((2x+h)/2)sin h/2}+hcos(x+h)]`
`=underset(hto0)"lim"[-2sin(x+h/2)(sinh/2)+cos(x+h)]`
`[therefore cosC-cosD=-2sin(C+D)/(2).sin(C-D)/2]`
`=2underset(hto0)"lim"xsin(x+h/2)underset(hto0)"lim"(sinh/2)/(h/2).1/2+underset(hto0)"lim"cos(x+h)`
=`-2.1/2xsinx+cosx`
`=cosx-xsinx`