Question: How differentiate and integrate a function of array variables ?

I have a function of array x[n]: f.e. f:= x[1] + x[1]*x[2] + x[1]*x[2]*x[3]. How to compute a derivative with respect to x[1],x[2],x[3] ? diff(f,x[1]) returns 0. Another question: I need to evaluate n- multidimensional integral: int... ( int( int(f,x[1]=0..1) , x[2]=0..1, ..... , x[n]=0..1 ). How shall I write ?
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