Giải bài 59 trang 117 SGK giải tích nâng cao 12

a) $y={{\log }_{3}}\left( \sin x \right)$

$y'=\dfrac{\left( \sin x \right)'}{\sin x\ln 3}=\dfrac{\cos x}{\sin x\ln 3} \\ y'\left( \dfrac{\pi }{4} \right)=\dfrac{1}{\ln 3}\approx 0,91$

b) $y=\dfrac{{{2}^{x}}}{{{x}^{2}}}$

$y'=\dfrac{{{2}^{x}}\ln 2.{{x}^{2}}-2x{{.2}^{x}}}{{{x}^{4}}}=\dfrac{{{2}^{x}}\left( x\ln 2-2 \right)}{{{x}^{3}}} \\ y'\left( 1 \right)=2\left( \ln 2-2 \right)\approx -2,61$