Question

найти производную функции

Answer 1

а) Найти производную

$((x^{3}+3)(x-x^{3}))' =(x^{3}+3)'(x-x^{3}) + (x^{3}+3)(x-x^{3})' = \\ \\ = 3x^{2}(x-x^{3}) + (x^{3}+3)(1-3x^{2}) = \\ \\ = 3x^{3}-3x^{5} + x^{3}-3x^{5} +3-9x^{2} = \\ \\ = 3-9x^{2} +4x^{3}-6x^{5}$

б) Найти производную

$( \frac{x^{4} - x^{2}}{x-1})' = \frac{(x^{4} - x^{2})'(x-1) - (x^{4} - x^{2})(x-1)'}{(x-1)^2} = \\ \\ = \frac{(4x^{3} - 2x)(x-1) - (x^{4} - x^{2})}{(x-1)^2} =\frac{(4x^{3} - 2x)(x-1) - x^{2} (x+1)(x-1)}{(x-1)^2} = \\ \\ = \frac{(4x^{3} - 2x)-x^{2} (x+1)}{(x-1)} = \frac{4x^{3}-2x-x^{3}-x^{2} }{(x-1)} = \frac{x(3x^{2}-x-2)}{(x-1)} = \\ \\ = \frac{x(x-1)(3x-2)}{(x-1)} = x(3x+2)$