Question

Найти производную функции
1)f (х)= 2/3 х³- х²-7х;

2) q(х)= 1/ х³ +7;

3) f(х)= (х+1)²(х-1)

4)q(х) = ctg²x - cos 2x.


СРОЧНО, ДАЮ 42 Б!!!

Answer 1

1) f'(x) = 2/3 * 3x² - 2x - 7 = 2x² - 2x - 7

2) q'(x) = -3x⁻⁴

3) f'(x) = 2(x+1)(x-1) + (x+1)² = 2x² - 2 + x² + 2x + 1 = 3x² + 2x - 1

4) q'(x) = 2ctgx(-1/sin²x) + 2sin2x = -cosx/sin³x + 2sin2x

(xⁿ)' = nxⁿ⁻¹

(uv)' = u'v + uv'