Question

find the derivative of y=ln2* log2 x

Answer 1

The books said the answer is 1/x but I got 1/2xln2 as my answer?

Answer 2

Change of base formula:\[\large\rm \log_2x=\frac{\ln x}{\ln 2}\]

Answer 3

Do you see how the ln(2)'s will cancel out?

Answer 4

wouldn't it be x/2 then?

Answer 5

oh wait a minute... ln 2* 1/x ln2= 1/x right?

Answer 6

I would recommend canceling them out `before` differentiating :)
Maybe will be easier to understand that way.\[\large\rm y=\ln2\cdot\color{orangered}{\log_2x}\]\[\large\rm y=\ln2\cdot\color{orangered}{\frac{\ln x}{\ln2}}\]\[\large\rm y=\ln x\]But yes, your way works fine as well :)

Answer 7

Thanks for explaining :)