Differentiate the following with respect to x.
(i) `4x^3 - 3x^2 +(4)/(x^2) -8`

Options

A. `12 x^3 - 6x -8x^(-3)`
B. `12 x^2 - 6x -8x^(-1)`
C. `12 x^2 - 4x -8x^(-3)`
D. `12 x^2 - 6x -8x^(-4)`

Answer

B

Explanation

(i) `y = 4x^3 - 3x^2 +(4)/(x^2) - 8`
`(dy)/(dt) = (d)/(dx) (4x^3 - 3x^2+(4)/(x^2) - 8) = (d)/(dx) (4x^3) - (d)/(dx) (3x^2) +(d)/(dx) ((4)/(x^2)) - (d)/(dx)(8)`
` = 4xx3x^(3-1) - 3xx2x^(2-1) +4(-2)x^(-2-1) - 0 =12 x^2 - 6x -8x^(-3) = 12x^2 -6x (8)/(x^3)`
(ii) ` y = 5x^4 +4x^(3//4) -3x^2+2x`
`(dy)/(dx) = (d)/(dx) (5x^4 + 4x^(3//4) - 3x^2 +2x) = (d)/(dx) (5x^4) +(d)/(dx)(4x^(3//4)) - (d)/(dx)(3x^2) + (d)/(dx)(2x)`
` = 5xx4 x^(4-1)+4xx(3)/(4)x ^((3)/(4)x-1) - 3xx2x^2 +2xx1 = 20x^3 +3x^(-1//4) - 6x +2`