Question

Find the derivative: g(x)=log2sqr.root(x). I've used the log. function and will comment the form I'm at now, but what next?

Answer 1

Find the derivative of: \[g(x)=\log_{2}\sqrt{x} \]
And this is where I'm at:
\[g'(x)=\frac{ \frac{ 1 }{ 2 }x^{-1/2}}{ (\ln 2)\sqrt{x} }\]

Answer 2

@agent0smith ....Have a bit of free time?

Answer 3

why not use change of base and make it a base e log function... then differentiate

Answer 4

so using change of base you get

\[\log_{2} (x^{\frac{1}{2}}) = \frac{\ln(x^{\frac{1}{2}})}{\ln(2)}\]

Answer 5

remember ln(2) is a constant

Answer 6

Oh my gosh I would have never thought of that

Answer 7

@campbell_st , how would you differentiate that?

Answer 8

use the chain rule

Answer 9

Personally, I'd use the properties of logarithms to turn
\[\log_{2} (x ^{1/2})=\frac{ 1 }{ 2 }\log_{2} (x) \]
Then I would differentiate it into
\[\frac{ 1 }{ 2x \ln(2) }\]

Answer 10

yes that's an easier way