1) f(x)=3x⁷-x⁵+x²+7 ⇒f¹(x)=3·7x⁶ -5x⁴+2x=21x⁶ -5x⁴+2x;
2) f(x)=4√x+√2-1/x³+1/x=4x^(¹/₂)+√2 -x⁻³+x⁻¹;⇒
f¹(x)=4·1/2x^(⁻¹/₂)-(-3)x⁻⁴+(-1)x⁻²=2/√x+3/x⁴-1/x²;
3)f(x)=(2x-x²)·(4x+3)=8x²-4x³+6x-3x²=-4x³+5x²+6x;⇒
f¹(x)=-4·3x²+5·2x+6=-12x²+10x+6;
4)f(x)=(6+x²)/(7x-5);⇒f¹(x)=((6+x²)¹·(7x-5)-(6+x²)(7x-5)¹)/(7x-5)²=
(2x·(7x-5)-(6+x²)·7)/(7x-5)²=(14x²-10x-42-7x²)/(7x-5)²=(7x²-10x-42)/(7x-5)²;