Найдите производную функции 1) f(x)=3x²[latex] \sqrt{x} [/latex] 2)f(x)=x²sinx 3)f(x)=[latex] \frac{ x^{2} -2}{x} [/latex] 4)f(x)=(2x-1)³ 5)f(x)=[latex] \sqrt{3x+2}[/latex] 6)f(x)=ctg[latex] \frac{x}{3} [/latex]

1) [latex]f(x)=3x^2*x^{ \frac{1}{2} }=3x^{2.5} \\ \\ f'(x)=3*2.5x^{1.5}=7.5x \sqrt{x} [/latex] 2) [latex]f'(x)=2xsinx+x^2cosx[/latex] 3) [latex]f'(x)= \frac{2x*x-(x^2-2)}{x^2}= \frac{2x^2-x^2+2}{x^2}= \frac{x^2+2}{x^2}=1+ \frac{2}{x^2} [/latex] 4) [latex]f'(x)=3(2x-1)^2*2=6(2x-1)^2[/latex] 5) [latex]f'(x)= \frac{3}{2 \sqrt{3x+2} } [/latex] 6) [latex]f'(x)=- \frac{1}{3sin^2 \frac{x}{3} } [/latex]