Найдите производную) 1. y=1/2x^3-2x^2+x+2 2. y=1/x^2 3. y=3x^2-2/x^3 4. y=sin(4x+П/6) :))

Question

Найдите производную)

1. y=1/2x^3-2x^2+x+2

2. y=1/x^2

3. y=3x^2-2/x^3

4. y=sin(4x+П/6)

:))

Answer 1

1. y = 0,5x³ - 2x² + x + 2

y' = 1,5 x² - 4x + 1

 

2. y = 1/x^2

y = x⁻²

y' = -2·x⁻³

y' = -2/x³

 

3. y=3x² - 2/x³

y = 3x² - 2·x⁻³

y' = 6x - 2·(-3)·x⁻⁴

y' = 6x + 6/x⁴

 

4. y = sin(4x + π/6)

y' = 4·cos(4x + π/6)

Answer 2

1. y=1/2x^3-2x^2+x+2

у' = (3/2)x² - 4x + 1

2. y=1/x^2

y' = -2/x³

3. y=3x^2-2/x^3

y'=6x-2*(-3)/x⁴ = 6x +6/x⁴

4. y=sin(4x+П/6)

y' = cos(4x+п/6)*4 = 4сos(4x+п/6)