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

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

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

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

true

used the chain rule

jc your answer is way off

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

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

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.

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