Question

Вычислите значение производной функции...

Answer 1

$1)quad y=frac{1}{2}tg(4x-pi )+frac{pi}{4}; ,; x_0=frac{pi}{4}\\y'=frac{1}{2}cdot frac{1}{cos^2(4x-pi )}cdot 4=frac{2}{cos^2(4x-pi )}\\y'(frac{pi}{4})=frac{2}{cos^20}=frac{2}{1}=2\\2)quad y=14sqrt{2x-3}; ,; ; x_0=26\\y'=14cdot frac{1}{2sqrt{2x-3}}cdot 2=frac{14}{sqrt{2x-3}}\\y'(26)=frac{14}{sqrt{49}}=frac{14}{7}=2\\3)quad y= frac{x-2}{x^2} \\y'= frac{x^2-(x-2)cdot 2x}{x^4} = frac{-x^2+4x}{x^4} =frac{4-x}{x^3}=0\\4-x=0\\x=4$