184.a)f'(x)=3(4+1/x²)²·(4+1/x²)'=3(4+1/x²)²·(-2/x³)= -6/x³(4+1/x²)².
б)f'(x)=2(5-4/x)·(5-4/x)'=8/x²·(5-4/x).
185.a)f'(x)=(12/(x-√x))'-(x²-12x+36)'=( 12'(x-√x)-12(x-√x)') / (x-√x)²=
(-12(1- 1 /2√x) /(x-√x)²=(-12+6/√x) /(x-√x)².
б)f'(x)=(10/(x+√x))' +((√x-1)³)'= (-10(1+ 1/2√x)) / (x+√x)² +3(√x-1)²·1/2√x=
(-10-5/√x) / (x+√x)²+1,5√x(√x-1)².
186.a)f'(x)=1/2√1-3x² ·(-6x)+ (-2x /(x²+4)²)=- 3x/√1-3x² - 2x /(x²+4)².
б)f'(x)=3(8-3x^6)²·(8-3x^6)'-(2x(5-x²)-x²·(-2x)) / (5-x²)²=
-54x^5·(8-3x^6)²- 10x /(5-x²)². (трудно будет разобраться!)
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Answers & Comments
184.a)f'(x)=3(4+1/x²)²·(4+1/x²)'=3(4+1/x²)²·(-2/x³)= -6/x³(4+1/x²)².
б)f'(x)=2(5-4/x)·(5-4/x)'=8/x²·(5-4/x).
185.a)f'(x)=(12/(x-√x))'-(x²-12x+36)'=( 12'(x-√x)-12(x-√x)') / (x-√x)²=
(-12(1- 1 /2√x) /(x-√x)²=(-12+6/√x) /(x-√x)².
б)f'(x)=(10/(x+√x))' +((√x-1)³)'= (-10(1+ 1/2√x)) / (x+√x)² +3(√x-1)²·1/2√x=
(-10-5/√x) / (x+√x)²+1,5√x(√x-1)².
186.a)f'(x)=1/2√1-3x² ·(-6x)+ (-2x /(x²+4)²)=- 3x/√1-3x² - 2x /(x²+4)².
б)f'(x)=3(8-3x^6)²·(8-3x^6)'-(2x(5-x²)-x²·(-2x)) / (5-x²)²=
-54x^5·(8-3x^6)²- 10x /(5-x²)². (трудно будет разобраться!)