second derivative

[rubing]

I am trying to find the second derivative of √(t / (t + 3))

For the first derivative I get using the quotient rule:

3/2 * t^-3/2 * (t+3)^-3/2 (multiplication signs added in for readability)

then the second derivative using the product rule comes out to:

-9/4 [ t^-5/2 * (t+3)^-3/2 + t^-3/2 * (t+3)^-5/2 ]

The answer key shows something extremely different. Am I doing something wrong?

 

[HallsofIvy]

Does the square root apply to the entire fraction so your function is \(\displaystyle t^{1/2}(t- 3)^{-1/2}\)?

Then you first derivative is incorrect. The derivative is \(\displaystyle (1/2)t^{-1/2}(t- 3)^{-1/2}- (1/2)t^{1/2}(t-3) ^{-3/2}\).

 

[rubing]

ahhhh...of course! I wasn't even thinking to break it up in that way, thanks so much!!!!!!!!!!!