# Differentiate the equation

• Aug 27th 2009, 04:40 PM
yoman360
Differentiate the equation
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: $\displaystyle y'=\frac{1}{3}x^{-2/3}$
• Aug 27th 2009, 04:41 PM
ynj
yes
• Aug 27th 2009, 05:25 PM
eXist
I disagree with the 2nd and the 4th problem.

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

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

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

4) $\displaystyle \frac{1}{2}t^{-1/2}+\frac{1}{2}t^{-3/2}$
• Aug 27th 2009, 05:30 PM
yoman360
Quote:

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

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

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

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

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