How do you differentiate $f(t)=(2t)/(2+sqrtt)$ ?

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Answer 1 · 2018-04-09T04:29:48

Using the quotient rule allows for this to be differentiated.

Quotient rule:
$f(x) = g(x)/(h(x))$
$f'(x) = (g'(x)h(x) - h'(x)g(x))/(h(x)^2)$

In your question:
$f(t) = (2t)/(2 + sqrt(t))$

$g(t) = 2t$
$h(t) = 2 + sqrt(t)$

$g'(t) = 2$
$h'(t) = 1/sqrt(t)$

This means that
$f'(t) = (2(2 + sqrt(t))- 1/sqrt(t)2t)/((2+sqrt(t))^2)$
$f'(t) = (4+ 2sqrtt - 2sqrtt)/((2+sqrt(t))^2)$

Final answer:
$f'(t) = 4/((2+ sqrtt)^2)$

How do you differentiate f(t)=(2t)/(2+sqrtt)f(t)=(2t)/(2+sqrtt)?