6)y=5sinx+√x 7)y= 6 --cosx x⁻³ 8)y=(x⁶+3)(x⁴-4) 9)y=√x(6x-1) 10)y=x⁶ cosx

1. \(y = 5\sin x + \sqrt{x}\)

   \(y' = (5\sin x)' + (\sqrt{x})'\)

   \(y' = 5\cos x + \frac{1}{2\sqrt{x}}\)

2. \(y = \frac{6}{x^{-3}} - \cos x\)

   \(y = 6x^3 - \cos x\)

   \(y' = (6x^3)' - (\cos x)'\)

   \(y' = 18x^2 + \sin x\)

3. \(y = (x^6 + 3)(x^4 - 4)\)

   \(y' = (x^6 + 3)'(x^4 - 4) + (x^6 + 3)(x^4 - 4)'\)

   \(y' = 6x^5(x^4 - 4) + (x^6 + 3)(4x^3)\)

   \(y' = 6x^9 - 24x^5 + 4x^9 + 12x^3\)

   \(y' = 10x^9 - 24x^5 + 12x^3\)

4. \(y = \sqrt{x}(6x - 1)\)

   \(y = 6x^{\frac{3}{2}} - \sqrt{x}\)

   \(y' = (6x^{\frac{3}{2}})' - (\sqrt{x})'\)

   \(y' = 6 \cdot \frac{3}{2}x^{\frac{1}{2}} - \frac{1}{2\sqrt{x}}\)

   \(y' = 9\sqrt{x} - \frac{1}{2\sqrt{x}}\)

5. \(y = x^6 \cos x\)

   \(y' = (x^6)' \cos x + x^6 (\cos x)'\)

   \(y' = 6x^5 \cos x - x^6 \sin x\)

Ответ: смотри решение выше