Thread: Derivatives of natural logarithms

I am just learning how to do these problems. I have to find the derivative of y with respect to t for

y= ln (t^2)

Can someone explain the formula for doing a problem like this?

Originally Posted by KarlosK

I am just learning how to do these problems. I have to find the derivative of y with respect to t for

y= ln (t^2)

Can someone explain the formula for doing a problem like this?

You are supposed to know that the derivative of is .

Since you don't have a single variable t you have to use

a) some laws of logaritm:

b) the chain rule:

Be aware that the logrithm function is only defined for positive arguments.

Originally Posted by KarlosK

I am just learning how to do these problems. I have to find the derivative of y with respect to t for

y= ln (t^2)

Can someone explain the formula for doing a problem like this?

Dear KarlosK,

You have to use,

1)

2)The Chain rule

Do you have any questions?? Please don't hesitate to ask!!

Originally Posted by earboth

You are supposed to know that the derivative of is .

Since you don't have a single variable t you have to use

a) some laws of logaritm:

b) the chain rule:

Be aware that the logrithm function is only defined for positive arguments.

In part a, I am having trouble seeing how you went from y=2 ln(t) to the y'= 2/t can you just explain that one step.

Also do you need to do both parts a/b, or is that just a way to check the answer? Thanks for the help!!

Originally Posted by KarlosK

In part a, I am having trouble seeing how you went from y=2 ln(t) to the y'= 2/t can you just explain that one step.

Also do you need to do both parts a/b, or is that just a way to check the answer? Thanks for the help!!

Dear KarlosK,

Do you know that, Thats what he had used when going from y=2 ln(t) to the y'= 2/t.

a) and b) are two methods of doing the same problem. You can do it anyway you wish.

Hope this helps.

Originally Posted by KarlosK

In part a, I am having trouble seeing how you went from y=2 ln(t) to the y'= 2/t can you just explain that one step.

Also do you need to do both parts a/b, or is that just a way to check the answer? Thanks for the help!!

Hi KarlosK, so taking the derivative of a natural logarithmic function is simply . In your case your would be simply . By chain rule, after taking the derivative of the first function, theres is a function within a function which is the , so there for it becomes . Yet, yielding the final solution as .