some calc questions

[JAZN 5,000+ posts]

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.

sin(x^2) = 2xcos(x^2)

(sinx)^2 = 2(cosx)(sinx)

Great time to ask about a test you're taking tomorrow, btw.

 

[electronicsgeek 10+ year member]

sin(x^2) = 2xcos(x^2)(sinx)^2 = 2(cosx)(sinx)

thats all i needed. help much appreciated JAZN

 

[electronicsgeek 10+ year member]

sin(x^2) =Great time to ask about a test you're taking tomorrow, btw.

dude why you going to give me that bullshit, everyone has their own way of studying and this is mine so keep it to your self buddy.

I already thank'd you didnt I!!!

 

[JAZN 5,000+ posts]

dude why you going to give me that bullshit, everyone has their own way of studying and this is mine so keep it to your self buddy.

I already thank'd you didnt I!!!

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[bdawson72 5,000+ posts]

Stop cryin u got help

 

[swimfreak26 10+ year member]

Just follow the chain rule very closely and you'll be able to do these things after a little effort.

The example of ln(x^2):

The derivitive is the derivitive of the inside multiplied by the derivitive of the function itself. Now, you know the deriv of ln(u) = u, and the derivitive of x^n = nx^(n-1).

So...

d/dx (ln(x^2)) = d/dx(x^2) * d/dx(ln(u)) where u is the quantity x^2

This gives you:

d/dx (ln(x^2)) = 2x/x^2 = 2/x

Now, follow the same set of rules for ln(x)^2, where now x is the quantity of "ln(x)" when doing the simple power rule.

So you get:

d/dx (ln(x)^2)) = (2)(ln(x))(1/x) = 2ln(x)/x

Don't know if that helps or not, but I hope so.

 

[negativezeroz 5,000+ posts]

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

well lnx^2 would take the ln of x then square that number...

ln(x^2) would be the ln of whatever x squared is...

i.e.: ln(5)^2 = ~2.59

ln(5^2) = ~3.21 (mind youi im using the calc on windows so if its wrong im not using my 83+ //content.invisioncic.com/y282845/emoticons/wink.gif.608e3ea05f1a9f98611af0861652f8fb.gif )