How can I verify my logarithmic differentiation for this function?

[K.QMUL]

1. The problem statement
Differentiate with respect to (x) the following function...

https://www.physicsforums.com/attachment.php?attachmentid=62329&stc=1&d=1380565485

*As you can see I attempted logarithmic differentiation but am unsure if I'm doing it right at the moment. Could someone send me an image of their calculations?

 

[Ray Vickson]

1. The problem statement
Differentiate with respect to (x) the following function...

https://www.physicsforums.com/attachment.php?attachmentid=62329&stc=1&d=1380565485

*As you can see I attempted logarithmic differentiation but am unsure if I'm doing it right at the moment. Could someone send me an image of their calculations?

Your attachment does not appear on my screen. Why don't you just type out the function?

Also: I don't think you should expect anyone to send you an image of their calculations. That is not supposed to be how this forum works.

 

[K.QMUL]

Sorry, its the following:

[(e^x)*sin(x)]/[(x^2)*cos(x)]

 

[Mark44]

Please show us the work that you did.

 

[K.QMUL]

Here is my working out so far, not sure if its correct though

 

[Mark44]

I see one mistake, right when you took the natural log of both sides ln(e^x) = x, not xln(e^x) as you have. The work below that is correct, though, so you must have intuitively used the correct value. Your answer looks fine.

One way to check your work is to use the quotient rule to see if you get the same result.