Question

Differentiate the following w.r.t.x
(1) `(3x +5)` (ii)` x^(-2)` (iii) `x^(3//2)` (iv) `sqrtx - (1)/(sqrtx)` (v) `(1)/((x +2))`

Answer 1

Correct Answer - `[(i) 3` (ii) `(-2)/(x^3)` (iii) `(3)/(2) s^(1//2)` (iv) `(1)/(2sqrtx) ((x +1)/(x))` (v) `-(1)/((x +2)^2)]`
(iv) `(d)/(dx) (sqrtx) - (d)/(dx)((1)/(sqrtx)) = (d)/(dx)(x^(1//2)) - (d)/(dx)(x^(-1//2)) = (1)/(2)x^(-1//2) = (1)/(2)x^(-3//2) = (1)/(2sqrtx)(1+(1)/(x)) = (1)/(2sqrtx) ((x +1)/(x))`
(v) `(d)/(dx)((1)/(x+2)) =(d)/(dx)(x + 2)^(-1) = (-1)(x+2)^(-2)(d)/(dx)(x+2) = -(1)/((x+2)^2) [1+0] = -(1)/((x+2)^2)`