Question

Найдите производную функции: f(x)=x³+x²
f(x)=√x(1-x)
f(x)=5/2x-3​

Answer 1

1.

$f(x) = {x}^{3} + {x}^{2} \\ f'(x) = 3 {x}^{2} + 2x$

2.

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

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

3.

$f(x) = \frac{5}{2x - 3} = 5 {(2x - 3)}^{ - 1}$

$f'(x) = - 5 {(2x - 3)}^{ - 2} \times (2x - 3)' = \\ = - 5 {(2x - 3)}^{ - 2} \times 2 = \\ = - \frac{10}{ {(2x - 3)}^{2} }$