# Finding the Derivative

1. Feb 14, 2009

### Jim4592

1. The problem statement, all variables and given/known data
Find ds/dt for s=(t2)(1/7)

2. Relevant equations
I attempted to find the answer by using the chain rule...

3. The attempt at a solution
ds/dt = (1/7)*(t2)-(6/7)*(2t)
ds/dt = (2/7)*t*(t2)-(6/7)

I belive that would be the answer but the problem is that the answer key in the book tells me that ds/dt = (2/7)t-(5/7)

I don't understand what they did to cancel out the t2 ang get the power to be -5/7

2. Feb 14, 2009

### mplayer

Simplify 's' first before you take the derivative. Remember the properties of exponents.

3. Feb 14, 2009

### Jim4592

thanks i got it now that i said s=t(2/7)

4. Feb 14, 2009

### Staff: Mentor

Your answer is correct, but it's not as simplified as it can be. Also, using the chain rule led to a lot of unnecessary work that could have been avoided by simplifying the expression first.

(2/7)*t*(t2)-(6/7)
=(2/7) *t* t-12/7
=(2/7) *t7/7* t-12/7
= (2/7) * t-5/7