The discussion revolves around differentiating the function f(t) = (t^5 + t^6 - 1) / t^7. Participants are exploring the appropriate methods for finding the derivative, particularly focusing on the use of the quotient rule and simplification techniques.
The conversation is ongoing, with some participants providing guidance on using the quotient rule and others suggesting that simplification may be a viable approach. There is no clear consensus on the best method yet, as different interpretations are being explored.
Some participants highlight the importance of recognizing the need for simplification before applying differentiation rules, while others emphasize the necessity of the quotient rule in this context. The original poster's understanding of the problem setup is also questioned.
nicksauce said:Or simply write it as the sum
t^-2 + t^-1 - t^-7
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.neutron star said: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?
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.fan_103 said:U must use quotient Rule!