Question

с производными Найти производную функции f(x) = (2x + 1)^5 − (2 − 3x)^3.

2. Найти производную функции f(x) = cos^2(x^4 − x^3 + 2).

3. Найти производную функции f(x) = (√(4x^2 + 3)) ∙ tg2x.

Answer 1

$1)f'(x) = 5 {(2x + 1)}^{4} \times 2 - 3 {(2 - 3x)}^{2} \times ( - 3) = 10 {(2x + 1)}^{4} + 9 {(2 - 3x)}^{2}$

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

$3)f'(x) = \frac{1}{2} {(4 {x}^{2} + 3)}^{ - \frac{1}{2} } \times 8xtg(2x) + \frac{1}{ { \cos }^{2}(2x) } \times 2 \sqrt{4 {x}^{2} + 3} = \\ = \frac{4xtg(2x)}{ \sqrt{4 {x}^{2} + 3} } + \frac{2 \sqrt{4 {x}^{2} + 3 } }{ { \cos}^{2}(2x) }$