Question

помогите с решением производных.
пишите подробно

Answer 1

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

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

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

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

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

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