👤

cum verific f'(×)din asta? f(×)=(×+2)^3

Cum Verific Fdin Asta F23 class=

Răspuns :

Aplici regula ridicarii la putere si obtii:


[tex] f'(x)=\frac{\mathrm{d}}{\mathrm{d}x}(x+2)^3=3(x+2)^2\cdot\frac{\mathrm{d}}{\mathrm{d}x}(x+2)[/tex]


Cum parametrul [tex]x[/tex] are derivata 1 si constanta [tex]2[/tex] are derivata [tex]0[/tex]:


[tex]f'(x)=3(x+2)^2=3(x^2+4x+4)=3x^2+12x+12\:\forall\: x\in \mathbb{R} [/tex]



f(x)=(x+2)³

f(x)'=3(x+2)²

(a+b)²=a²+2ab+b²

f(x)'=3(x+2)²=3(x²+4x+4)=3x²+12x+12

f(x)'=3x²+12x+12