Question

Найдите прoизвoдную от функции $y=f(x)$, когда a)$f(x)=x^{4}-3x^{3}+\frac{1}{2}x^{2}+48$
b)$f(x)=x^{3}+\frac{2}{x^{2}}-18x$

Answer 1

Объяснение:

$a)f(x) = {x}^{4} - 3 {x}^{3} + \frac{1}{2} {x}^{2} + 48$

$f'(x) = 4 {x}^{3} - 3 \times 3 {x}^{2} + \frac{1}{2} \times 2x + 0 = \\ = 4 {x}^{3} - 9 {x}^{2} + x$

$b)f(x) = {x}^{3} + \frac{2}{ {x}^{2} } - 18x = \\ = {x}^{3} + 2 {x}^{ - 2} - 18x$

$f'(x) = 3 {x}^{2} + 2 \times ( - 2) {x}^{ - 3} - 18 = \\ = 3 {x}^{2} - \frac{4}{ {x}^{3} } - 18$