Question

Найти производную сложной функции f(x)= (3 – 2х)^3

Answer 1

f(x) = (3 - 2x)³

f'(x) = 3(3 - 2x)² * (3 - 2x)' = 3 * (- 2) * (3 - 2x)² = - 6(3 - 2x)²

Answer 2

Ответ:

$- 6(2x - 3) {}^{2}$

Объяснение:

$f(x) = (3 - 2x) {}^{3} \\ f'(x) = \frac{d}{dx} ((3 - 2x) {}^{3} ) \\ f'(x) = \frac{d}{dg} (g {}^{3} ) \times \frac{d}{dx} (3 - 2x) \\ f'(x) = 3g {}^{2} ( - 2) \\ f'(x) = 3(3 - 2x) {}^{2} ( - 2) \\ f'(x) = - 24x {}^{2} + 72x - 54 \\ f'(x) = - 6(2x - 3) {}^{2}$