Answer:
1)
a. 18x²-8
b. f'(x) = 6x²+20x+1
c. [tex]\frac{2\sqrt{x} +4}{\sqrt{x} }[/tex]
2)
a.[2(x-1)-2x]/(x-1)²
b. [(4x+3)(x²+1)-(2x)(2x²+3x-2)]/(x²+1)²
Step-by-step 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) = [tex]\frac{\sqrt{x}+3 }{\sqrt{x} }[/tex]+ [tex]\frac{\sqrt{x} +1}{\sqrt{x} }[/tex] = [tex]\frac{2\sqrt{x} +4}{\sqrt{x} }[/tex]
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
