Verified answer

1. f(x)=6x⁴-x²/2-7x+10

f'(x)=24x^3-2x/2-7=24x^3-x-7

2. f(x)=4/x³-5/x²=4x^(-3)-5x^(-2)

(x^a)'=ax^(a-1)

f'(x)=-12x^(-4)+10x^(-3)=2x^(-3)(5-6/x)

3. f(x)=(5x-1)*√x

f'(x)=5√x+(5x-1)/2√x=(10x+5x-1)/2√x=(15x-1)/2√x