some calc questions

[electronicsgeek 10+ year member]

whats the diffrence between ln(x^2) and lnx^2? Say we try to take the derivitive. How would it matter?

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[JimJ 5,000+ posts]

Graph them; you get extremely different graphs //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif

 

[electronicsgeek 10+ year member]

Graph them; you get extremely different graphs //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif

yes but how would that show a diffrence in numerical value, if you took the derivitive of it?

same thing with tan(x^4) and tanx^4? whats the diffrence? whats the derivitive of both?

 

[JimJ 5,000+ posts]

They have different domains and ranges...for example, you have a limit @ X=0 for [ln(x)]^2, while you have negative values for X for the other one.

Don't know if that helps or not.

I believe they're both derived using the chain rule, but I'm not really an expert on this by any means, I'm barely passing my calc class as it is //content.invisioncic.com/y282845/emoticons/biggrin.gif.d71a5d36fcbab170f2364c9f2e3946cb.gif

 

[electronicsgeek 10+ year member]

They have different domains and ranges...for example, you have a limit @ X=0 for [ln(x)]^2, while you have negative values for X for the other one.
Don't know if that helps or not.

I believe they're both derived using the chain rule, but I'm not really an expert on this by any means, I'm barely passing my calc class as it is //content.invisioncic.com/y282845/emoticons/biggrin.gif.d71a5d36fcbab170f2364c9f2e3946cb.gif

uhhhhhh

could you do this, probably make things much easier for both of us. wahts the derivative of ln(x^2) and lnx^2? and tan(x^4) and tanx^4? it will make things much clearer for me.

 

[electronicsgeek 10+ year member]

*bump*

 

[ndnbolla 10+ year member]

First of all the derivative of ln (x) is 1/x , right?

So then:

ln (x^2) = ln (x) + ln (x) so derivative of this is simply 1/x + 1/x .

In the other case (ln(x))^2 = ln(x) * ln(x) and the derivative of this using the chain rule would be:

(1/x * ln(x) + ln(x) * 1/x) = (ln (x) / x) + (ln (x) / x) = 2ln(x)/(x)

Not too sure on all of this since I haven't taken any calc in a while though.

 

[electronicsgeek 10+ year member]

bump

 

[electronicsgeek 10+ year member]

*bump*

 

[electronicsgeek 10+ year member]

*bump for help*

 

[electronicsgeek 10+ year member]

bumpers for help

 

[LuNaTiC 10+ year member]

ln(x^2) and lnx^2 are very diff statements, therefore, the derivitive does matter...

 

[electronicsgeek 10+ year member]

ln(x^2) and lnx^2 are very diff statements, therefore, the derivitive does matter...

care to answere what the derivative of both of those are? or better yet tan(x^2) andd tanx^2?

 

[Acidburn 5,000+ posts]

care to answere what the derivative of both of those are? or better yet tan(x^2) andd tanx^2?

cant do your own homework?

 

[electronicsgeek 10+ year member]

cant do your own homework?

haah...its actually not my hw. im studying for a calc1 test tom. iv been confused with this basic rule how to simplfiy this function.

find dy/dx:

sin(x^2)=2xcosx^2?

sinx^2=2xcosx^2?

are those correct? cant be.