Question

Please help me with this

Answer 1

a.
`(2(x-6)(x-2))/((x^2+4)^2)`

Explanation:

a. f'(x) =
`(x(3x-2))/(x^2+4)`

b. f'(x) =
`(2(x^2-6x-1))/((x-3)^2)`

using quotient rule and product rule

f'(x) =
`([(3x-2)+3x](x^2+4)-(2x)[x(3x-2)])/((x^2+4)^2)`

f'(x) =
`((6x-2)(x^2+4)-2x(3x^2-2x))/((x^2+4)^2)`

f'(x) =
`((6x^3-2x^2+24x-8)-(6x^3-4x^2))/((x^2+4)^2)`

f'(x) =
`(2x^2+24x-8)/((x^2+4)^2)` =
`(2(x-6)(x-2))/((x^2+4)^2)`

b. f'(x) =
`([(2x-1)+2(x+1)](x-3)-(x+1)(2x-1))/((x-3)^2)`

f'(x) =
`((4x+1)(x-3)-(x+1)(2x-1))/((x-3)^2)`

f'(x) =
`((4x^2-11x-3)-(2x^2+x-1))/((x-3)^2)`

f'(x) =
`(2x^2-12x-2)/((x-3)^2)`

f'(x) =
`(2(x^2-6x-1))/((x-3)^2)`