Expert: Paul Klarreich - 8/27/2009

Question
Hi! I'm in Calculus 1, and I'm just learning to find derivitives. I came across the following problem:
y=√(2x) + 2√(x), and I am asked to find the first derivitive.
Do I write the radicals as exponents? I am a little unsure how to do this. I would appreciate a step-by-step explanation! Thank you so much!

Answer
Questioner: Rebecca
Country: United States
Category: Calculus
Private: No
Subject: Finding Derivitives
Question: Hi! I'm in Calculus 1, and I'm just learning to find derivatives. I came across the following problem:
y=√(2x) + 2√(x), and I am asked to find the first derivative.
Do I write the radicals as exponents? I am a little unsure how to do this. I would appreciate a step-by-step explanation! Thank you so much!
...................................
yes, you do:

sqrt(x) = x^(1/2).

Then do

y = sqrt(2x) + 2 sqrt(x)

y = sqrt(2) sqrt(x) + 2 sqrt(x)

y = sqrt(2) x^(1/2) + 2 x^(1/2)

then use your  x^n rule.  Remember about constant coefficients.

And, please, show enough respect for mathematics to spell the vocabulary words correctly.