Question

Вычислить производные

Answer 1

$1)\; \; f(x)=(5x^4-4x^5)^9\\\\f'(x)=9(5x^4-4x^5)^8\cdot (20x^3-20x^4)\\\\2)\; \; f(x)=(7x^3-3x^7)^{10}\\\\f'(x)=10(7x^3-3x^7)^9\cdot (21x^2-21x^6)\\\\3)\; \; f(x)=\sqrt{3x^2-6x}\\\\f'(x)=\frac{1}{2\sqrt{3x^2-6x}}\cdot (6x-6)=\frac{3(x-1)}{\sqrt{3x^2-6x}}\\\\4)\; \; f(x)=\sqrt{x^3-3x}\\\\f'(x)=\frac{1}{2\sqrt{x^3-3x}}\cdot (3x^2-3)=\frac{3(x^2-1)}{2\sqrt{x^3-3x}}$

$5)\; \; f(x)=\frac{1}{4x-x^2}\\\\f'(x)=-\frac{4-2x}{(4x-x^2)^2}=\frac{2(x-2)}{(4x-x^2)^2}\\\\6)\; \; f(x)=\frac{1}{x^2-3x}\\\\f'(x)=-\frac{2x-3}{(x^2-3x)^2}=\frac{3-2x}{(x^2-3x)^2}$