Question

Помогите с математикой
Найти производную каждой функции:
1. (4cos x+3tg x)'
2. (2x^3*sin x)'
3. ((5x^4-2)*cos x)'
4. (3+2x/x-2)'

Answer 1

Ответ:

1.

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

2.

$(2 {x}^{3} \times \sin(x) )' = (2 {x}^{3} )' \times \sin(x) + (\sin(x)) '\times 2 {x}^{3} = \\ = 6 {x}^{2} \sin(x) + \cos(x) \times 2 {x}^{3}$

3.

$((5 {x}^{4} - 2) \times \cos(x))' = \\ (5 {x}^{4} - 2)' \times \cos(x) + ( \cos(x)) ' \times (5 {x}^{4} - 2) = \\ = 20 {x}^{3} \cos(x) - \sin(x) \times (5 {x}^{4} - 2)$

4.

$( \frac{3 + 2x}{x - 2} )' = \frac{(3 + 2x)'(x - 2) - (x - 2)'(3 + 2x)}{ {(x - 2)}^{2} } = \\ = \frac{2(x - 2) - (3 + 2x)}{ {(x - 2)}^{2} } = \frac{2x - 4 - 3 - 2x}{ {(x - 2)}^{2} } = \\ = - \frac{7}{ {(x - 2)}^{2} }$