# Strange derivative problem

1. Oct 18, 2009

### neutron star

1. The problem statement, all variables and given/known data
$$f(t)=\frac{t^5 + t^6 - 1}{t^7}$$

2. Relevant equations

3. The attempt at a solution
This is different than the other problems I've been doing.

My first guess would be that I would do this:
$$f(t)=\frac{5t^4 + 6t^5}{7t^6}$$
Is that the final answer or is there another step I need to do?

2. Oct 18, 2009

### whs

3. Oct 18, 2009

### nicksauce

Or simply write it as the sum

t^-2 + t^-1 - t^-7

4. Oct 18, 2009

### neutron star

Hey, thanks that was really helpful! I didn't think of dividing by t^7.

That made it easy! Thank you! I'll remember this if I get another similar problem!

5. Oct 19, 2009

### Staff: Mentor

As already noted, this is wrong. If you carried out this differentiation without simplifying first, you would need to use the quotient rule. whs has already provided a link to an article on differentiation rules, so I won't give that link again. The upshot is that if f(x) = g(x)/h(x), f'(x) is NOT equal to g'(x)/h'(x), which is precisely what you did.

6. Oct 19, 2009

### fan_103

U must use quotient Rule!

7. Oct 19, 2009

### Staff: Mentor

That's not necessary in this problem. As nicksauce already suggested, the OP can carry out the division and then use the sum rule and the power rule.