Differentiate the following functions with respect to `x `
`(xsinx+cosx)(e^x+x^x+logx)`

Explanation

Let u=(xsinx+cosx) and `v=(e^x+x^x+logx)`

`u'=(xcosx+sinx)-sinx`
`=xcosx`

`v'=e^x+x+2xlogx`

using the product rule

`(d/dx)(uv)=uv'+vu'`

=`(d/dx)(xsinx+cosx)(e^x+x^x+logx)=(xsinx+cosx)(e^x+x+2xlogx)+(e^x+x^2+logx)(xcosx)`