anonymous
  • anonymous
what is the derivative of 2t/(2+sqrt t) please detail information is needed i spent many times i know it is product rule yet i cannot find the answer on the back of the book.
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katieb
  • katieb
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blues
  • blues
You should use the quotient rule, not the product rule...
anonymous
  • anonymous
yes i did used it yet i cannot find the answer
blues
  • blues
If you express the equation in the form f(x) = g(x) / h(x), g(x) = 2t and h(x) = 2 + sqrt(t). So g'(x) = 2 and h'(x) = t^(-1/2). Did you get that far?

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anonymous
  • anonymous
it does not say find T it just says find the derivative
blues
  • blues
Yup. When you use the quotient rule to find a derivative, you have to start by identifying the numerator and the denominator. In this case the numerator, g(t) = 2t. The denominator, h(t) = (2 + t^1/2). Once you have done that, you have to find expressiosn for the derivatives of the numerator and denominator separately. That is, you have to find g'(t) and h'(t). Have you done that? If so, what did you get? Once you have that, the next step is to put them together...
anonymous
  • anonymous
g(t)=2 and h(t) =1/t^1/2
blues
  • blues
g(t) = 2t and g'(t) = 2. h(t) = 2 + t^1/2 and h'(t) = (1/2) t^(-1/2). You forgot to bring the (1/2) out in front of the t and it is easier to express 1/(t^1/2) as t^(-1/2). Cool?
anonymous
  • anonymous
waaw thank you very much
blues
  • blues
Can you take it from here?
anonymous
  • anonymous
yes lol thank you
blues
  • blues
Cool. :D
anonymous
  • anonymous
nice question aswell nice ans....

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