Question

Даю 85 баллов
Найти производную сложной функции
1) Y = 3^x * sin4x
2)Y = (X ― ^4 ― 25)^8
3)Y = x^4 / ln2

Answer 1

Ответ:

1.

$y = {3}^{x} \times \sin(4x)$

$y '= ( {3}^{x} ) '\times \sin(4x) + ( \sin(4x))' \times {3}^{x} = \\ = ln(3) \times {3}^{x} \times \sin(4x) + \cos(4x) \times 4\times {3}^{x} = \\ = {3}^{x} ( ln(3) \times \sin(4x) + 4\cos(4x) )$

2.

$y = {(x- {x}^{4} - 25)}^{8}$

$y' = 8 {( x-{x}^{4} - 25) }^{7} \times (x- {x}^{4} - 25)' = \\ = 8 {( x-{x}^{4} - 25) }^{7} \times (1-4 {x}^{3} )$

3.

$y = \frac{ {x}^{4} }{ ln(2x) }$

$y' = \frac{({x}^{4})'\times ln(2x)-(ln(2x))' \times {x}^{4} }{ ln^{2}(2x)}= \\= \frac{4{x}^{3}ln(2x)-\frac{1}{2x}\times 2 \times {x}^{4}}{ln^{2}(2x)} =\\=\frac{4x^{3}ln(2x)-x^{3}}{ln^{2}(2x)}$