467. Find the differentials of the functions:
a) $y=\sqrt{x^{3}-3}$
b) $y=\frac{x-1}{x+2}$
c) $y=x(x+1)$.
Solution. a) $d y=\frac{3 x^{2}}{2 \sqrt{x^{3}-3}} d x$;

b) $d y=\frac{(x-1)^{\prime}(x+2)-(x+2)^{\prime}(x-1)}{(x+2)^{2}} d x=\frac{(x+2)-(x-1)}{(x+2)^{2}} d x=$ $=\frac{3}{(x+2)^{2}} d x=\frac{3 d x}{(x+2)^{2}}$

c) $d y=\left(x^{\prime}(x+1)+(x+1)^{\prime} x\right) d x=(x+1+x) d x=(2 x+1) d x$.

468-477. Find the differentials of the functions: