Question

Найдите производные y=arccos4x^3
y=2arcsin9x^4
y=(x^3-3/x^2+4)^2
y=e^sinx ×arccos3x
y=5^6x × arcsin5x

Answer 1

1.

$y' = - \frac{1}{ \sqrt{1 - 16 {x}^{6} } } \times 12 {x}^{2} \\$

2.

$y '= \frac{2}{ \sqrt{1 - 81 {x}^{8} } } \times 36 {x}^{3} = - \frac{72 {x}^{3} }{ \sqrt{1 - 81 {x}^{8} } } \\$

3.

$y' = 2( {x}^{3} - \frac{3}{ {x}^{2} } + 4) \times ( 3{x}^{2} + 6 {x}^{ - 3} ) = \\ = 2( {x}^{3} - \frac{3}{ {x}^{2} } + 4)(3 {x}^{2} + \frac{6}{ {x}^{3} } )$

4.

$y' = {e}^{ \sin(x) } \times \cos(x) \times arccos3x - \frac{3}{ \sqrt{1 - 9 {x}^{2} } } \times {e}^{ \sin(x) } \\$

5.

$y'=ln(5) \times {5}^{6x} \times 6 \times arcsin(5x) + \frac{5}{ \sqrt{1 - 25 {x}^{2} } } \times {5}^{6x} \\$