Question

Найдите производную
1)f(x)=(2x-5)(5+2x) ,f '(-1)
2)f(x)=2√X*(5-x), f ' (5)
3)f(x)=$\frac{6x-3}{5-3x}$ , f '(2)
4)f(x)=$\frac{ x^{2} }{x-1}$ , f ' (0)

Answer 1

$f(x=(2x-5)(5+2x) \\ \\ f'(x)=2(5+2x)+2(2x-5)=10+4x+4x-10=8x \\ \\ f'(-1)=-8$


$f(x)=2 \sqrt{x} (5-x) \\ \\ f'(x)=2* \frac{1}{2} * \frac{5-x}{ \sqrt{x} } -2 \sqrt{x} = \frac{5-3x}{ \sqrt{x} } \\ \\ f'(5)= \frac{5-15}{ \sqrt{5} } = \frac{-10}{sqrt{5} }$

$f(x)= \frac{6x-3}{5-3x} \\ \\ f'(x)= \frac{6(5-3x)+3(6x-3)}{(5-3x)^2} = \frac{21}{(5-3x)^2} \\ \\ f'(2)= \frac{21}{(5-6)^2} =21$

$f(x)= \frac{x^2}{x-1} \\ \\ f'(x)= \frac{2x(x-1)-x^2}{(x-1)^2} = \frac{x^2-2x}{(x-1)^2} \\ \\ f'(0)=0$