Question

найдите производные функции

$f(x) = {x}^{2} (x + 2) \\ f(x) = {x}^{3} + 2 {x}^{2} + x + 30$
$f(x) = \sqrt{4 - 3 {x}^{2} } \\ f(x) = \cos(2 {x}^{2} - 3x + 1 )$

Answer 1

$f'(x) = (x^2(x+2))' = (x^2)'(x+2)+x^2(x+2)' = \\ \\ = 2x(x+2) + x^2 *1= 3x^2+4x$

или

$f'(x) = (x^2(x+2))' = (x^3 +2x^2)' = 3x^2 + 4x$


$f'(x) = (x^3 +2x^2 +x +30)' = 3x^2 +4x +1$


$f'(x) = (\sqrt{4-3x^2} )' = (4-3x^2)^{ \frac{1}{2} } = \frac{1}{2} (4-3x^2)^{ \frac{1}{2} -1} (4-3x^2)' = \\ \\ =\frac{1}{2} (4-3x^2)^{ -\frac{1}{2}} (-6x) = -\frac{3x}{ \sqrt{4-3x^2} }$


$f'(x) = (cos(2x^2+3x+1))' = -sin(2x^2+3x+1) * (2x^2+3x+1)' = \\ \\ = -sin(2x^2+3x+1) * (4x+3)$