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Решите задачу:

$1) y`=( \frac{ x^{3}+16}{x})`=[( \frac{u}{v})`= \frac{u`\cdot v-u\cdot v`}{v^{2} } ]= \frac{ (x^{3}+16)`\cdot x- ( x^{2}+ 16)\cdot x`}{ x^{2} } = \\= \frac{ (3x^{2})\cdot x- ( x^{2}+ 16)\cdot 1}{ x^{2} } = \frac{ 3x^{3}- x^{2}-16}{ x^{2} }$
$2) y`=[(u\cdot v)`=u`\cdot v+u\cdot v`]=(2x)`\cdot ln(e- \frac{2}{x})+2x\cdot (ln(e- \frac{2}{x})`= \\ =2\cdot ln(e- \frac{2}{x})+2x\cdot \frac{1}{e- \frac{2}{x} }\cdot(e- \frac{2}{x})` = \\ =2\cdot ln(e- \frac{2}{x})+2x\cdot \frac{1}{e- \frac{2}{x} }\cdot(0-(- \frac{2}{x^{2} })) = \\ =2\cdot ln(e- \frac{2}{x})+2x\cdot \frac{x}{ex-2 }\cdot\frac{2}{x^{2} }= \\ =2\cdot ln(e- \frac{2}{x})+ \frac{4}{ex-2 }$
$3)y`= \frac{(e ^{x})`\cdot x- e ^{x}\cdot(x)`}{ x^{2} }= \frac{(e ^{x})\cdot x- e ^{x}\cdot 1}{ x^{2} }= \frac{(e ^{x})\cdot( x- 1)}{ x^{2} }$
$4) y`=-sin(ln ^{2}x)\cdot (ln ^{2}x)`=-sin(ln ^{2}x)\cdot 2ln x\cdot(lnx)`= \\ =- sin(ln ^{2}x)\cdot 2ln x\cdot \frac{1}{x} =- \frac{sin(ln ^{2}x)\cdot 2ln x}{x}.$