# Math Help - Differentiate the equation

1. ## Differentiate the equation

Did I differentiate these correctly?

1) $g(x)=5x^8-2x^5+6$
my answer: $g'(x)=40x^7-10x^4$

2) $f(t)=\frac{1}{2}t^6-3t^4+t$
my answer: $f'(t)=3t^5-12t+1$

3) $R(t)=5t^{-3/5}$
my answer: $-3t^{-8/5}$

4) $f(t)=\sqrt{t}-\frac{1}{\sqrt{t}}$
my answer: $\frac{1}{2}t^{-1/2}+\frac{1}{2}t^{-2/3}$

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

2. yes

3. I disagree with the 2nd and the 4th problem.

You have:
2) ...
my answer: $f'(t)=3t^5-12t+1$

4) ...
my answer: $\frac{1}{2}t^{-1/2}+\frac{1}{2}t^{-2/3}$

I think it should be:
2) $f'(t)=3t^5-12t^3+1$

4) $\frac{1}{2}t^{-1/2}+\frac{1}{2}t^{-3/2}$

4. Originally Posted by eXist
I disagree with the 2nd and the 4th problem.

You have:
2) ...
my answer: $f'(t)=3t^5-12t+1$

4) ...
my answer: $\frac{1}{2}t^{-1/2}+\frac{1}{2}t^{-2/3}$

I think it should be:
2) $f'(t)=3t^5-12t^3+1$

4) $\frac{1}{2}t^{-1/2}+\frac{1}{2}t^{-3/2}$