Question

Найти производную 1) y=3x^5+2x-2 2) y=(3/x)+3√x 3) y=√x×(5-2x^2) 4) y=(cosx)/x^2 5) y=(2x^2+4)/√x 6) y=(tgx)/3x

Answer 1

1) y=3x^5+2x-2
y' = 15x^4 +2
2) y=(3/x)+3√x
y' = -3/x² + 3/(2√x)
3) y=√x*(5-2x^2)
y' = 1/(2√x) * (5 -2x²) + √x * (-4x) = (5 -2x² -8x²)/(2√x) = (5 -10x²)/(2√x)
4) y=(cosx)/x^2
y' = (-Sinx*x² - Cosx *2x)/x^4
5) y=(2x^2+4)/√x
y' = (4x*√x - (2x² +4)*1/(2√x) )/x = (8x²-2x² -4)/(2x√x) = (6x² -4)/(2x√x)
6) y=(tgx)/3x

Answer 2

1. y' = 15x^4 + 2

2. y' = -3/x^2 + (3/2)x^(-1/2)

3. y' = (5-2x^2)/(2√x) - x(5-2x^2)/(2x√x)

4. y' = -[(sinx)/x^2] - 2(cosx)/x^3

5. y' = (4x-1)/(x√x)

6. y' = [3sec^2(x) - (tgx)(6x)] / 9x^2