Differentiate the following function with respect of `x :(sin x-xcos x)/(xsinx+cosx)`

Explanation

Let `f(x)=(xsinx-cosx)/(sinx+xcosx​)` which is of the form u/v


`f′(x)=(u′v−v′u)/v^2`
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=`(xsinx+cosx)(d/dx)​(sinx−xcosx)−(sinx−xcosx)(d/dx)​(xsinx+cosx)​))/(xsinx+cosx)^2`


=`(xsinx+cosx)(cosx−cosx+xsinx)−(sinx−xcosx)(xcosx+sinx−sinx)​/(xsinx+cosx)^2`

=`((xsinx+cosx)(xsinx)−(sinx−xcosx)(xcosx)​)/(xsinx+cosx)^2`


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