Найти производную [latex]1)\frac{15}{(6x-4)^{10}}[/latex] 2)[latex]y=x^{x} [/latex] 3)y=[latex]y=\frac{x^{2}+1}{x+1} [/latex] 4)y=[latex]y=\frac{5}{x^{2}}[/latex] 5)[latex]2x^{3}-x+\pi[/latex]

1) [latex](\frac{15}{(6x-4)^{10}})'=(15(6x-4)^{-10})'=\\ 15*((6x-10)^{-10})'=\\ 15*\frac{(6x-10)^{-10-1}}{-10-1}*(6x-10)'=\\ \frac{-15}{11(6x-4)^{11}}*6=-\frac{90}{11(6x-10)^{11}}[/latex]   2) [latex]y=x^x=e^{x ln x} [/latex] [latex]y'=(e^{xlnx})'=(e^{xlnx})*(xln x)'=x^x*( x(ln x)'+(x)'ln x)=x^x*(x*\frac{1}{x}+1*ln x)=x^x*(ln x+ 1)[/latex]   3) [latex]y=\frac{x^2+1}{x+1}[/latex] [latex]y'=(\frac{x^2+1}{x+1})'=\frac{(x^2+1)'*(x+1)-(x^2+1)*(x+1)'}{(x+1)^2}=\\ \frac{2x*(x+1)-(x^2+1)*1}{(x+1)^2}=\frac{2x^2+2x-x^2-1}{(x+1)^2}=\frac{x^2+2x-1}{x^2+2x+1}[/latex]   4) [latex]y=\frac{5}{x^2}[/latex] [latex]y'=(\frac{5}{x^2})'=(5x^{-2})'=5(x^{-2})'=5*\frac{x^{-2-1}}{-2-1}=-\frac{5}{3x^3}[/latex]   5) [latex](2x^3-x+\pi)'=(2x^3)'-(x)'+(\pi)'=2(x^3)'-1+0=2*3x^2-1=6x^2-1[/latex]