ПОМОГИТЕ!!! , F(x)=1+x^3 , x0=1, найдите производную по определению

$F(x)=1+x^3$
$F(x_0)=1+x^3_0$
$\Delta x=x-x_0$
$\Delta f(x)=f(x)-f(x_0)=(1+x^3)-(1+x^3_0)=1+x^3-1-x^3_0=\\\\x^3-x^3_0=(x-x_0)(x^2+xx_0+x^2_0)$
$\frac{\Delta f(x)}{\Delta x}=\frac{(x-x_0)(x^2+xx_0+x_0)}{x-x_0}=x^2+xx_0+x^2_0$

x_0} \frac{\Delta f(x)}{\Delta x}=lim_{x->x_0} (x^2+xx_0+x^2_0)=3x^2_0" alt="lim_{x->x_0} \frac{\Delta f(x)}{\Delta x}=lim_{x->x_0} (x^2+xx_0+x^2_0)=3x^2_0" align="absmiddle" class="latex-formula">
$f'(x)=3x^2$