Partial derivatives of the natural logs

[claratanone]

Find the partial derivatives of the following function:

Q=(1/3)log_eL+(2/3)log_eK

Any help would be much appreciated!

Below is my working out so far:

$$\frac{\partial Q}{\partial L}= \frac{\frac{1}{3}}{L}$$

$$\frac{\partial Q}{\partial K}= \frac{\frac{2}{3}}{L}$$

Are these correct?

 

[MarkFL]

I suspect it is just a typo, but you want:

$$\pd{Q}{K}=\frac{\frac{2}{3}}{K}=\frac{2}{3K}$$