Question

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.

Answer 1

You should use the quotient rule, not the product rule...

Answer 2

yes i did used it yet i cannot find the answer

Answer 3

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?

Answer 4

it does not say find T it just says find the derivative

Answer 5

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...

Answer 6

g(t)=2 and h(t) =1/t^1/2

Answer 7

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?

Answer 8

waaw thank you very much

Answer 9

Can you take it from here?

Answer 10

yes lol thank you

Answer 11

Cool. :D

Answer 12

nice question aswell nice ans....