Question

1.5 Решите пожалуйста производную. Срочно!!!1

Answer 1

1.1 f(x)`=(2*√x³-3*∛x²+6*∛x)`=2*(3/2)*x¹/²-3*(2/3)*x⁻¹/³+6*(1/3)*x⁻²/³=
=3*1-2*1+2*1=3.
1.2 f(x)`=2x/(1+x²)=((2x)`*(1-x²)-2x*(1+x²)`)/(1+x²)²=(2-4x²)/(1+x²)²=
=(2-4*(-3))/(1+(-3)²)²=14/100=0,14.
1.3 f(x)`=((x-1)*√(x²+1))`=(x-1)`*√(x²+1)+(x-1)*(√(x²+1))`=
=1*√(x²+1)+(x-1)*(1/2)*(x²+1)⁻¹/²*2x=
=1*√(0²+1)+(0+1)*(1/2)*(0²+1)⁻¹/²*2*0=1.
1.6 f(x)`=(√e⁵ˣ)`=(e²,⁵ˣ)`=2,5*e²,⁵ˣ=2,5*e²,⁵*⁰=2,5*1=2,5.
1.4 f(x)`=((1/3)*cos³x-cosx)`=(1/3)*3*cos²x*(-sinx)-(-sinx)=
=-cos²x*sinx+sinx=-cos²(π/6)*sin(π/6)+sin(π/6)=-(√3/2)²*(1/2)+1/2=
-3/8+1/2=1/8.