Solving a Strange Derivative Problem

[neutron star]

Homework Statement

$$f(t)=\frac{t^5 + t^6 - 1}{t^7}$$

Homework Equations

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?

 

[whs]

That is quite wrong.

http://www.mathwords.com/d/derivative_rules.htm

Check number 7, the quotient rule.

 

[nicksauce]

Or simply write it as the sum

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

 

[neutron star]

Or simply write it as the sum

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

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!

 

[Mark44]

$$f(t)=\frac{t^5 + t^6 - 1}{t^7}$$

The Attempt at a Solution

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?

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.

 

[fan_103]

U must use quotient Rule!

 

[Mark44]

U must use quotient Rule!

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.