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

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calyne
 3 years ago
Best ResponseYou've already chosen the best response.0y' = [(2x)/(ln(10)*sqrt(x)] + [2*log[10](sqrt(x))]

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0or no the derivative of log[10](sqrt(x)) would be (1/[sqrt(x)ln(10)])*(1/[2sqrt(x)])

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0well according to the textbook the answer is pretty different

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0alright well i've got 1/ln(10) + 2*log[10](sqrt(x))

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0that's not final though so help me from there

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0somehow the second term (after the +) needs to equal log[10](x) does that make sense

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.0isn't it something like this http://www.wolframalpha.com/input/?i=d%2Fdx%28+2x*log+base+10+%28sqrt%28x%29%29%29

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0sure i guess it's something like that bro jesus you're a great help

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0but that's still not the textbook answer

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.0let 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.

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0alright here look the textbook answer is 1/ln(10) + log[10](x).

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.0i got almost same answer ... except 1/ln(10) + 2log[10](x)

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0i 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

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0nah 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.....

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.0use 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.

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0i know that, and it still doesn't explain how 2*log[10](sqrt(x)) = log[10](x).

calyne
 3 years ago
Best ResponseYou've already chosen the best response.0oh unless... that equals log[10]([sqrt(x)]^2) ???? is that it?
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