Did I differentiate these correctly?

1) $\displaystyle g(x)=5x^8-2x^5+6$

my answer: $\displaystyle g'(x)=40x^7-10x^4$

2) $\displaystyle f(t)=\frac{1}{2}t^6-3t^4+t$

my answer: $\displaystyle f'(t)=3t^5-12t+1$

3) $\displaystyle R(t)=5t^{-3/5}$

my answer: $\displaystyle -3t^{-8/5}$

4) $\displaystyle f(t)=\sqrt{t}-\frac{1}{\sqrt{t}}$

my answer: $\displaystyle \frac{1}{2}t^{-1/2}+\frac{1}{2}t^{-2/3}$

5) $\displaystyle y=x^{1/3}$

my answer: $\displaystyle y'=\frac{1}{3}x^{-2/3}$