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Ответ:

Производная дроби:  [tex]\bf \Big(\dfrac{u}{v}\Big)'=\dfrac{u'v-uv'}{v^2}[/tex]  ,

производная произведения :  [tex]\bf (uv)'=u'v+uv'[/tex]   .

[tex]1a)\ \ y=\dfrac{lnx}{1-x}\\\\\\y'=\dfrac{(lnx)'\cdot (1-x)-lnx\cdot (1-x)'}{(1-x)^2}=\dfrac{\dfrac{1}{x}\cdot (1-x)-lnx\cdot (-1)}{(1-x)^2}=\\\\\\=\dfrac{1-x+x\cdot lnx}{x\cdot (1-x)^2}=\dfrac{1+x\cdot (lnx-1)}{x\cdot (1-x)^2}\\\\\\b)\ \ y=\dfrac{1}{x^3}-2x^5\\\\y'=-\dfrac{1\cdot 3x^2}{x^6}-2\cdot 5x=-\dfrac{3}{x^4}-10x[/tex]    

[tex]c)\ \ y=\Big(\dfrac{x}{3}-7\Big)^6\\\\y'=6\cdot \Big(\dfrac{x}{3}-7\Big)^5\cdot \cfrac{1}{3}=2\cdot \Big(\dfrac{x}{3}-7\Big)^5\\\\\\d)\ \ y=e^{x}\cdot sinx\\\\y'=(e^{x})'\cdot sinx+e^{x}\cdot (sinx)'=e^{x}\cdot sinx+e^{x}\cdot (-cosx)=e^{x}\cdot (sinx-cosx)[/tex]