Question

How do you differentiate `f(x)=xsinx` using the product rule?

Answer 1

hi
PRODUCT RULE SAYS
if to diffrentiate "uv"( here i will take w.r.t to x)
i.e
`d((uv))/dx`=`u*d(v)/dx`+`v*du/dx`
i.e u must know
diffrentiation of `x^n`=`nx^(n-1)`
here..,

**diffrentiation of x=(1)`x^(1-1)` =1

diffrentiation of" sinx" is "`cos x`"

NOW,
`dx.sin(x)/dx`=`(x).dsin(x)/dx`+`(sinx)(d(x)/dx)` = xcos(x)+sin(x)
=
So diffrentiation of F(X)=x sin(x)-=x cos(x)+sin(x)

Answer 2

`f'(x)=xcosx+sinx`

Explanation:

`"given "f(x)=g(x)h(x)" then"`

`f'(x)=g(x)h'(x)+h(x)g'(x)larrcolor(blue)"product rule"`

`g(x)=xrArrg'(x)=1`

`h(x)=sinxrArrh'(x)=cosx`

`rArrf'(x)=xcosx+sinx`