Question

СРОЧНО ПОМОГИТЕ С ПРОИЗВОДНОЙ

Answer 1

f(x) =2x∛x² +4/(x⁴*√x²) =2*(x^(1+2/3) )+ 4/(x^5) =2*(x^(5/3) ) +4*(x^(- 5)) ;
f '(x) =( 2*(x^(5/3) ) + 4*(x^(- 5)) ) ' =(  2*(x^(5/3) ) )' + (4*(x^(- 5)) ) ' =
2*(x^(5/3) ) ' +4*(x^(- 5)) ' =2*(5/3)* x^(5/3 -1) +4*(-5)*x^(-5 -1)=
2*(5/3)* x^(2/3) +4*(-5)*x^(-6) = (10/3)*∛x² -20/x⁶ .

f '(1) =(10/3)*∛1² -20/1⁶ =10/3 -20 = -50/3.