Question

differentiate y=log2 x

Answer 1

\[y= \log_{2} x\]

Answer 2

Hey Dan, remember your change of base formula? :)\[\large\rm \log_b(a)=\frac{\ln(a)}{\ln(b)}\]

Answer 3

yes but i dont think i understand how to do it. I get lnx/ln2 and then i dnot know what to do after that

Answer 4

Ok great.
Let's pull the numerical portion out front,\[\large\rm \frac{\ln x}{\ln2}\quad=\quad \left(\frac{1}{\ln2}\right)\ln x\]

Answer 5

Even though this coefficient looks very strange and complicated,
it's just a NUMBER.

Think of it like this,\[\large\rm (5)x\]You remember how to differentiate that, yes?

Answer 6

how did you pull the numerical portion out i dont understand that

Answer 7

\[\large\rm \frac{1}{\ln2}\cdot \ln x\quad=\quad \frac{1}{\ln2}\cdot\frac{\ln x}{1}\quad=\quad \frac{1\cdot \ln x}{\ln2\cdot 1}\]If you follow these steps in reverse, then it might make some sense.

I split it into two fractions, using fraction multiplication.
You have to artificially create a 1 in the top and bottom for it to work out nicely.

Answer 8

Woops I meant to say (5)ln x in the previous comment,
no big deal though.

Answer 9

okay

Answer 10

\[\large\rm \frac{d}{dx}(\text{#})\ln x\]So we have some weird looking number times our log.
Remember how to differentiate your natural log? :)

Answer 11

yes i think

Answer 12

i;m not sure how to continue

Answer 13

What is the derivative of ln x?

Answer 14

1/x

Answer 15

1/x (1)

Answer 16

Ok good.

So if we had 5lnx, we we would end up with 5(1/x) right?

Answer 17

yes

Answer 18

The 5 can come outside of the differentiation process since it is a constant coefficient.\[\large\rm \frac{d}{dx}5\ln x=5\frac{d}{dx}\ln x=5\frac{1}{x}\]

Same thing happens with our problem,\[\large\rm \frac{d}{dx}\left(\frac{1}{\ln2}\right)\ln x=\left(\frac{1}{\ln2}\right)\frac{d}{dx}\ln x=?\]

Answer 19

(1/ln2)(1/x)

Answer 20

Yayyy good job!

We can combine the fractions as a last step perhaps,
just so it looks a little nicer,\[\large\rm =\frac{1}{x \ln2}\]

Answer 21

thank youuu, i will work on practice problems for this to see if i understand it better I will be back if i am stuck

Answer 22

cool