Question

Сросшиеся кости нижней части ноги птицы образуют

Answer 1

$(x^ \alpha )`= \alpha x^{ \alpha -1} \\\ (e^x)`=e^x \\\ (\cos x)`=-\sin x \\\ (\ln x)`= \frac{1}{x} \\\ (\log_ \alpha x)`= \frac{1}{x\ln \alpha } \\\ (ab)`=a`b+ab` \\\ ( \frac{a}{b} )`= \frac{a`b-ab`}{b^2}$

$y= \frac{2}{x} -3 \sqrt[4]{x^2}= 2x^{-1} -3x^{0.5} \\\ y`= -2x^{-2} -1.5x^{-0.5} = -\frac{2}{x^2} - \frac{1.5}{ \sqrt{x} }$

$y=9( \frac{x}{3} +5)=3x+45 \\\ y`=3$

$y=e^x\cos x \\\ y`=(e^x)`\cos x+e^x(\cos x)`=e^x\cos x-e^x\sin x=e^x(\cos x-\sin x)$

$y= \frac{\ln x}{1-x} \\\ y`=\frac{(\ln x)`(1-x)-(\ln x )(1-x)`}{(1-x)^2} =\frac{ \frac{1}{x} (1-x)+\ln x }{(1-x)^2} =\frac{ \frac{1}{x} -1+\ln x }{(1-x)^2}$

$y=\log_2(x^2+3) \\\ y`= \frac{(x^2+3)`}{(x^2+3)\ln2} = \frac{2x}{(x^2+3)\ln2} \\\ y`(1)= \frac{2\cdot 1}{(1^2+3)\ln2} = \frac{2}{4\ln2} =\frac{1}{2\ln2}$