Question

Please help me with this

Answer 1

1)

a. 18x²-8

b. f'(x) = 6x²+20x+1

c.
`(2√(x) +4)/(√(x) )`

2)

a.[2(x-1)-2x]/(x-1)²

b. [(4x+3)(x²+1)-(2x)(2x²+3x-2)]/(x²+1)²

Explanation:

1)

a. f(x) = 2x(3x²-4)

f'(x) = 2(3x²-4)+(6x)(2x)

f'(x) = 6x²-8+12x² = 18x²-8

b. f'(x) = (2x²+1)+(4x)(x+5)

f'(x) = 2x²+1+4x²+20x

f'(x) = 6x²+20x+1

c. f'(x) =
`(√(x)+3 )/(√(x) )`+
`(√(x) +1)/(√(x) )` =
`(2√(x) +4)/(√(x) )`

2.

a. f'(x) = [2(x-1)-2x]/(x-1)²

b. f'(x) = [(4x+3)(x²+1)-(2x)(2x²+3x-2)]/(x²+1)²