1.

Differentiate the following with respect to x. (i) `(4 x +2)(5x^2 +4)` (ii) `(2x^3 _3) (2x^(-3) +1)`

Answer» (i) `y = (4x +2)(5x^2+4)`
`(dy)/(dx) = (4x +2) (5x^2+4)`
`(dy)/(dt) = (4x+2) (d)/(dx) (5x^2+4)+(5x^2+4) (d)/(dx) (4x+2)`
`=(4x+2)xx(5xx2x^(2-1) + 0) + (5x^2 +4) (4xx1x^(1-1) +0)`
`=(4x+2)10x+(5x^2+4) 4 = 40x^2 +20x +20 x^2 +16`
`= 60x^2 + 20x+16`
(ii) `y = (2x^3+3)(2x^(-3) +1)`
`(dy)/(dx) = (2x^3 +3) (d)/(dx)(2x^(-3) +1) (2x^(-3) +1) (d)/(dx) (2x^3+3)`
`=(2x^3+3)[2xx(-3)x^(-3-1) +0] + (2x^(-3) +1) (2xx3x^(3-1) +0)`
`=(2x^3 + 3)((-6)/(x^4)) +((2)/(x^3) +1) 6x^2 = (-12)/(x) - (18)/(x^4) +(12)/(x) + 6x^2`
`=6x^2 - (18)/(x^4)`


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