Finding the Limit of tln(t) as t Approaches 0

[mattmns]

Is the derivative of sin(3x) just 3sin(3x) because of the chain rule? IE, let u=3x, then 3sin(u) => 3sin(3x)

Thanks.


Ok, I am pretty sure that is true. How about, <br /> <br /> \lim_{t\rightarrow 0} tln(t)<br /> <br />

What is the common approach for this problem?

 

[OlderDan]

Is the derivative of sin(3x) just 3sin(3x) because of the chain rule? IE, let u=3x, then 3sin(u) => 3sin(3x)

Thanks.


Ok, I am pretty sure that is true. How about, <br /> <br /> \lim_{t\rightarrow 0} tln(t)<br /> <br />

What is the common approach for this problem?

It's not true because the derivative of sine is not itself

For the limit, you might look for a minimum of the function. Does it have one? More than one? That should get you started.

 

[p53ud0 dr34m5]

i agree with OlderDan.
h(x)=f(g(x))
if you have that, then:
h&#039;(x)=f&#039;(g(x))*g&#039;(x)
so, sine is not the derivative of itself.

 

[mrjeffy321]

I think the derivative of sine is cosine,
so the derivative of sin(3x) would be 3cos(3x)

 

[mattmns]

Bah, that is what I meant, sorry. Thanks, been a while since I did a derivative or a limit