What is the simplified derivative of (50t)/(6+t)^3?

[939]

Homework Statement

I keep getting it wrong. Using the quotient rule.

Homework Equations

Derivative of (50t)/(6+t)^3

The Attempt at a Solution

My answer: -100t^3 - 900t^2 + 10800/((6+t)^3)^2)
The book: (-100 (t - 3))/(6 + t)^4

What happened?



EDIT: Nevermind, I realize they're basically the same. I'll leave this here incase someone needs help in the future.

 

[jedishrfu]

how did you arrive at your answer? did you use the product rule?

with y=u v then dy/dx = du/dx .v + u . dv/dx

i get the book answer

 

[Mark44]

Homework Statement

I keep getting it wrong. Using the quotient rule.

Homework Equations

Derivative of (50t)/(6+t)^3

The Attempt at a Solution

My answer: -100t^3 - 900t^2 + 10800/((6+t)^3)^2)
The book: (-100 (t - 3))/(6 + t)^4

What happened?



EDIT: Nevermind, I realize they're basically the same. I'll leave this here incase someone needs help in the future.

To get the book's answer, don't multiply things out in the numerator after you use the quotient rule. In the numerator, both terms have a factor of 50 and a factor of (6 + t)². Bring out these factors, and what you have left is easy to simplify, and results in the book's answer.