Question

Find the derivative of the function.
r(t) = log_4(t + sqrt(t))

My answer (sorry, it's messy):
(1+(1/2sqrt(t)))(1/tln(4)+sqrt(t)ln(4))

Answer 1

recall that
y = log_a u
y' = (1/lna)*(1/u)*(du/dy)
I will assume that you have
r(t) = log₄ (t + √t)

r ' (t) = (1/ln4)*( 1/(t + √t) )*(1 + (1/2)t^(-1/2) )
= (1/ln4) (1 + 1/(2√t) )/(t + √t)
if we multiply top and bottom by 2√t

= (1/ln4) (2√t + 1)/(2t^(3/2) + 2t)

or variations of that

Answer 2

As I read your solution, it appears to be correct.

I think this is what you meant, the second term is the denomiator... (1+(1/2sqrt(t)))/( (tln(4)+sqrt(t)ln(4)) )

Answer 3

Yes, that's what I meant. :) Thank you both!