Differentiate :
(i) `(e^(x))/(x)` , (ii) `((2x+3)/(x^(2) - 5))` , (iii) `(e^(x))/((1+sinx))`

Explanation

(i) `d/(dx)(e^(x)/(x)) = (x.(d)/(dx) (e^(x)).(d)/(dx)(x))/(x^(2)) = (xe^(x) - e^(x).1)/(x^(2)) = (e^(x)(x-1))/(x^(2))`
(ii) `(d)/(dx) ((2x+3)/(x^(2) -5 ) = (x^(2) -5) .(d)/(dx) (2x+3) -(2x+3) .(d)/(dx) (x^(2) - 5))/((x^(2) -5)^(2))`
`= ((x^(2) - 5).2-(2x+3).2x)/((x^(2) - 5)^(2)) = (-2(x^(2) + 3x+5))/((x^(2) -5)^(2))`
(iii) `(d)/(dx) ((e^(x))/(1+sinx)) = ((1+sinx).d/(dx)(e^(x))- e^(x).(d)/(dx) (1+sinx))/(1+sinx)^(2)`
`= ((1+sinx).e^(x)-e^(x)(cosx))/((1+sinx)^(2)) = ((1+sinx - cosx)e^(x))/((1+sinx)^(2))`