Question

Differentiate the following with respect to x.
(i) `x^6` (ii) `(1)/(x^3)` (iii) `sqrtx`

Answer 1

(i) `y = x^6 , (dy)/(dx) = 6x^(6-1) = 6x^5` (ii) `y = (1)/(x^3) = x^(-3) , (dy)/(dx) = (-3)x^(-3-1) = -3x^(-4) = (-3)/(x^4)`
(iii) `y = sqrtx = x^(1/2) , (dy)/(dx) = (1)/(2) x ^(((1)/(2)-1)) = (1)/(2)x ^(-(1)/(2)) = (1)/(2sqrtx)`