Question

Найдите производную функцию, помогите

Answer 1

7)

$y = (2x-1)^6\\\\y' = (2x-1)'\cdot 6(2x-1)^5 = 2\cdot 6(2x-1)^5 = \boxed{\bf{12(2x-1)^5}}$

8)

$y = \sqrt{x^3-3x}\\\\y' = (x^3-3x)'\cdot \dfrac{1}{2\sqrt{x^3-3x}} = (3x^2 - 3)\cdot\dfrac{1}{2\sqrt{x^3-3x}} = \boxed{\bf{\dfrac{3x^2 -3}{2\sqrt{x^3-3x}}}}$

9)

$y = \log_{3}(2x^2-3x+1)\\\\y' = (2x^2-3x+1)' \cdot \dfrac{1}{\ln3(2x^2-3x+1)} = \boxed{\bf{\dfrac{4x - 3}{\ln3(2x^2-3x+1)}}}$

10)

$y = 14^{2-5x}\\\\y' = (2-5x)'\ln14\cdot 14^{2-5x} = \boxed{\bf{-5\ln14\cdot14^{2-5x}}}$

11)

$y = x^3 + \ln(6x-1)\\\\y' = (x^3)' + (\ln(6x-1))' = 3x^2 + (6x-1)'\cdot \dfrac{1}{6x-1} = \boxed{\bf{3x^2 + \dfrac{6}{6x-1}}}$

12)

$y = \dfrac{3}{x} - \dfrac{2}{x^2} + \dfrac{4}{x^5}\\\\\\y = 3x^{-1} - 2x^{-2} + 4x^{-5}\\\\y' = (3x^{-1})' - (2x^{-2})' + (4x^{-5})' = 3\cdot (-1)\cdot x^{-2} - 2\cdot (-2)\cdot x^{-3} +\\\\+ 4\cdot(-5)\cdot x^{-6} = -3x^{-2} + 4x^{-3} - 20x^{-6} = \boxed{\bf{-\dfrac{3}{x^2} + \dfrac{4}{x^3} - \dfrac{20}{x^6}}}$