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

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