Thread: deriv. of ln

The question is find derivative of
f(x) = sin(2ln x)

So far, I've worked it out till here:

cos(2lnx)(2/x+lnx)

Is that correct? If so, how can I simplify it more?

Originally Posted by kwivo

The question is find derivative of
f(x) = sin(2ln x)

So far, I've worked it out till here:

cos(2lnx)(2/x+lnx)

Is that correct? If so, how can I simplify it more?

no. the derivative of lnx is just 1/x

I'm sorry. Math is not my best subject. So if I ask some pretty simple questions, excuse me.

Ok, so is the cos(2lnx) part right? And for the inside function 2lnx, I didn't really know what to do with the 2 there. I know that the derivative of lnx is 1/x, but since the 2 was there, I used the product rule...which I guess is wrong?

Originally Posted by kwivo

I'm sorry. Math is not my best subject. So if I ask some pretty simple questions, excuse me.

Ok, so is the cos(2lnx) part right? And for the inside function 2lnx, I didn't really know what to do with the 2 there. I know that the derivative of lnx is 1/x, but since the 2 was there, I used the product rule...which I guess is wrong?

you don't use the product rule when you have a constant in front, the constant just stays there. and even if you did use the product rule, the derivative of a constant is zero, so it would wipe out the extra part. the derivative of 2ln(x) is simply 2/x

Ok, thanks for the clarification. So, it is cos(2lnx)(2/x). Is there a way to simplify more?

Originally Posted by kwivo

Ok, thanks for the clarification. So, it is cos(2lnx)(2/x). Is there a way to simplify more?

no, not really. i'd probably write 2cos(2lnx)/x

Originally Posted by Jhevon

no, not really. i'd probably write 2cos(2lnx)/x

I would hope you would write:

2 cos(2 ln(x)) / x

I hate function arguments just placed next to the function name, its sloppy. Also extra speces make things easier to read!

RonL