Найдите производные следующие функции:
1) y=(3-2x^3 )^5
2) y=(x^4-x-1)^4
3) y= √(x^3+1)
4) y= ^3√((1-x^2 )^2 )
5) y=2*cos5x
6) y=ln(sinx)
7) y=ln^3(x^2-1)
8) y = ln(ln^35x)

1)[tex](3-2x^{3})^{5}=5(3-2x^{3})^{4}((3-2x^{3}))'=-10(3-2x^{3})^{4}*( x^{3} )'[/tex]
[tex]=-30x^{2}(3-2x^{3})^{4}[/tex]
2)[tex]=4(x^{4}-x-1)^{3}*(x^{4}-x-1)'=4(x^{4}-x-1)^{3}*(4 x^{3} -1)[/tex]
3)[tex] (\sqrt{x^{3}+1})'= \frac{3x^{2}}{2 \sqrt{x^{3}+1} } [/tex]
4)[tex]= \frac{(1- x^{2} )^{2}'}{3((1- x^{2} )^{2})^ \frac{2}{3} } = \frac{2(1- x^{2} )*(1- x^{2} )'}{3((1- x^{2} )^{2})^ \frac{2}{3} } =[/tex]
[tex]= \frac{4x(1- x^{2} )}{3((1- x^{2} )^{2})^ \frac{2}{3} } [/tex]
5)[tex](2cos5x)'=-10sin5x[/tex]
6)[tex]ln(sinx)'=?[/tex]
7)[tex]ln^{3}( x^{2} -1)'=3ln^{2}( x^{2} -1)*ln( x^{2} -1)'=[/tex]
[tex]=3ln^{2}( x^{2} -1)* \frac{( x^{2} -1)'}{ x^{2} -1} =\frac{6x*ln^{2}( x^{2} -1) }{ x^{2} -1} [/tex]
8)[tex]ln(ln^{35}x)'=35*ln(lnx)'=35 \frac{lnx'}{lnx} = \frac{1}{x} * \frac{35}{lnx} [/tex]