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

1 Answer
Apr 9, 2018

Using the quotient rule allows for this to be differentiated.

Explanation:

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)#