Question

HELP ME PLEASE!
Show how to find the derivative of f(t)= t^2+1/t using the quotient rule. Then show how to find the derivative of the same function without using the quotient rule and first changing the form of the function. I get two different answers when I do this! HELP MEEEEEEEE

Answer 1

the answer to the first part is \[2t + \frac{(t)(0) - 1(1)}{t^2}\] Simplify and you get \[2t - \frac{1}{t^2}\]

Answer 2

its this all over t or just
\[f(t)=t^2+\frac{1}{t}\]

Answer 3

because if so you would not use the quotient rule the derivative of
\[t^2\] is
\[2t\] and the derivative of
\[\frac{1}{t}\] is
\[-\frac{1}{t^2}\]

Answer 4

Now doing it without the quotient rule you first need to write 1/t in exponential form.. So the new function would look like this \[t^2 + t^{-1}\] Now use the power rule to find the derivative. \[2t + -1t^{-2}\] Simplify and you get \[2t - t^{-2}\] or \[2t - \frac{1}{t^2}\]. So you get the same answer.

Answer 5

Thank you sooooooooooo much, it was on my take home test! :)