Question

Find d/dt ((2t^2+5t)/(t^5))^4

Answer 1

4{[(2t^2+5t)/(t^5)]^3} [(4t+5)(t^5)-(2t^2+5t)(5t^4)]/[(t^5)^2]

Answer 2

4t+5(t^5)-4(t^5)^3(5t^4)/(((t^5)^4)^2)

Answer 3

Since everything is to the 4th power, you have to use chain rule first. Then you differentiate everything that's inside.

Answer 4

true

Answer 5

used the chain rule

Answer 6

jc your answer is way off

Answer 7

lol what about mine?
i combined chain rule and quotient rule

Answer 8

answer is -4((2t^2+5t)/t^5)^3((6/t^4+20/t^5))
Parentheses might be messed up :-)

Answer 9

Akileez, I'm afraid your answer isn't correct either.Let me show each step needed to solve this problem.
First, let's say that f(t)= (2t^2+5t)/(t^5). Thus, the question is d/dt f(t)^4
You use the chain rule: 4 [f(t)^3] f'(t)
Plug in f(t): 4 [(2t^2+5t)/(t^5)]^3 f'(t).... Note that the quotient rule must be used here
4 {[(2t^2+5t)/(t^5)]^3} {[(t^5)(4t+5)-(2t^2+5t)(5t^4)]/(t^5)^2}
Simplify: -8 (2t+5)^3 [(3t+10)/(t^17)]

This answer was checked with a differentiation calculator.