Question

a derivada da cadeia da função f(x)=(2x-1/3x²+x-2)³

Answer 1

f(x)=1/27x^6+2/3x^5-28/9x^4+40/3x^3-76/3x^2+24x-8

Answer 2

$(2x- \frac{1}{3} x^2+x-2)^3 = \\ \\ =3 (2x- \frac{x}{3} ^{2}+x-2 )^{3-1}. (2x- \frac{ x^{2} }{3} +x-2)'= \\ \\ 3 (2x- \frac{x}{3} ^{2}+x-2 )^{2}. (2- \frac{2x}{3} +1)= \\ \\ 3(- \frac{ x^{2} }{3} +3x-2)^2.( \frac{6-2x+3}{3})= \\ \\ =3(- \frac{ x^{2} }{3} +3x-2)^2.( \frac{9-2x}{3})= \\ \\ = 3(- \frac{ x^{2} }{3} +3x-2)^2.( 3- \frac{2x}{3} )=3(3- \frac{2x}{3} )( -\frac{ x^{2} }{3} +3x-2)^2= \\ \\= (9-2x).(- \frac{ x^{2} }{3} +3x-2)^2$