Question

Find the derivative of f(t) = sqrt((2t+1)/(t^2+2))

Answer 1

you're going to have to either use product by bringing your denominator up or use quotient... which do you want to

Answer 2

... not getting answer must be afk

Answer 3

(y=f(t)) i like to find y' here by taking natural log of both sides

Answer 4

interesting lets see where you are getting at this lol

Answer 5

\[\ln(y)=\ln(\sqrt{\frac{2t+1}{t^2+2}})\]
\[\ln(y)=\frac{1}{2} [\ln|2t+1|-\ln(t^2+2)]\]
now find y' by doing first taking derivative of both sides
\[\frac{y'}{y}=\frac{1}{2}[\frac{2}{2t+1}-\frac{2t}{t^2+2}]\]

Answer 6

now simply multiply y on both sides

Answer 7

and replace y with \[\sqrt{\frac{2t+1}{t^2+2}} \]

Answer 8

and done

Answer 9

-(2/((t²+2)²))(t²+t-2) is the answer

Answer 10

if you want you can use algebra to show that if that is indeed the answer

Answer 11

take my expression and make it into that expression by using algebra manipulation

Answer 12

i didnt see sqrt. -(1/(√(2t+1)(t²+2)²))(3t²+2t-2)

Answer 13

this must be correct ans

Answer 14

http://www.wolframalpha.com/input/?i=Find+the+derivative+of++sqrt%28%282t%2B1%29%2F%28t^2%2B2%29%29

Answer 15

thanks guys this problem is a pain

Answer 16

really this problem shouldn't be that hard if you just move the bottom up by giving it a negative exponent and do the product rule

basically with something like this instead of the quotient rule which is just the product rule written another way, i go through these steps

1)Take the denominator and make it a numerator with negative exponent
2)Do product rule
3)After product rule, move the negative exponents back to the denominator
4)Usually after this step you can easily make a common denominator, do that
5)Add like terms and simplify the numerator
6)Profit

Answer 17

your way to approach this problem is very good,
thanks for the help

Answer 18

i still like my way much more :)