Mathematics 45 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

true

OpenStudy (anonymous):

used the chain rule

OpenStudy (anonymous):

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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.