Question

Найти производную 3x/cosx e'2x√2x-3 cos'2x-sin'2x x'2+1/x'3-x 2x'3-1/x'2

Answer 1

$1)\; \; y= \frac{3x}{cosx} \\\\y'= \frac{3\cdot cosx-3x\cdot (-sinx)}{(cosx)^2} = \frac{3(cosx+x\, sinx)}{cos^2x} \\\\2)\; \; y=e^{2x}\cdot \sqrt{2x-3}\\\\y'=2e^{2x}\cdot \sqrt{2x-3}+e^{2x}\cdot \frac{2}{2\sqrt{2x-3}} =2e^{2x}\cdot \Big (\sqrt{2x-3}+ \frac{1}{\sqrt{2x-3}} \Big )\\\\3)\; \; y=cos^2x-sin^2x\; \; \to \; \; y=cos2x\\\\y'=-2sin2x\\\\4)\; \; y=\frac{x^2+1}{x^3-x}\\\\y'= \frac{2x(x^3-x)-(x^2+1)\cdot (3x^2-1)}{(x^3-x)^2}\\\\5)\; \; y=\frac{2x^3-1}{x^2} =2x- \frac{1}{x^2} \\\\y'=2-\frac{-2x}{x^4}=2+\frac{2}{x^3}$