## calyne Group Title Differentiate the function y = 2x*log[10](sqrt(x)) 2 years ago 2 years ago

1. calyne Group Title

y' = [(2x)/(ln(10)*sqrt(x)] + [2*log[10](sqrt(x))]

2. calyne Group Title

correct so far?

3. calyne Group Title

or no the derivative of log[10](sqrt(x)) would be (1/[sqrt(x)ln(10)])*(1/[2sqrt(x)])

4. calyne Group Title

no it's not

5. calyne Group Title

well according to the textbook the answer is pretty different

6. calyne Group Title

alright well i've got 1/ln(10) + 2*log[10](sqrt(x))

7. calyne Group Title

that's not final though so help me from there

8. calyne Group Title

somehow the second term (after the +) needs to equal log[10](x) does that make sense

9. experimentX Group Title

isn't it something like this http://www.wolframalpha.com/input/?i=d%2Fdx%28+2x*log+base+10+%28sqrt%28x%29%29%29

10. calyne Group Title

sure i guess it's something like that bro jesus you're a great help

11. calyne Group Title

but that's still not the textbook answer

12. experimentX Group Title

let me test, dy/dx = 2{dx/dx*log[10](sqrt(x))+x*d(log[10](sqrt(x)))/dx} = 2{log[10](sqrt(x))+x*d(ln(sqrt(x)))/dx*1/ln10} = 2{log[10](sqrt(x))+x*1/sqrt(x)*1/2*1/sqrt(x)*1/ln10} = 2{log[10](sqrt(x))+1/2ln10} my answer.

13. calyne Group Title

alright here look the textbook answer is 1/ln(10) + log[10](x).

14. experimentX Group Title

i got almost same answer ... except 1/ln(10) + 2log[10](x)

15. calyne Group Title

i got as far as 1/ln(x) + 2(log[10](x)), the latter of which = 2[log(sqrt(x))/log(10)], so [2*log(sqrt(x))] / log(10) = log(sqrt(x))^2/log(10) ?? which = log(x)/log(10)? which = log[10](x) ???? is that correct? does that make sense? i'm reeeal rusty on the log business

16. calyne Group Title

nah bro according to the product rule that other end of the + sign is gonna be the derivative of 2x * the log[10](sqrt(x)). unless that's not the case. but i'm pretty sure it is. don't see any way around it really. and you got the derivative of 2x multiplying the other factor which is supposed to be left as is, so.... you tell me..... if and how i'm wrong.....

17. experimentX Group Title

use this property of log to convert it into natural log. $\log_ax = \frac{\ln x}{\ln a}$ I think there's a better example at wikipedia.

18. calyne Group Title

i know that, and it still doesn't explain how 2*log[10](sqrt(x)) = log[10](x).

19. calyne Group Title

oh unless... that equals log[10]([sqrt(x)]^2) ???? is that it?

20. calyne Group Title

oh so it is