differentiating logs

Questions
1

Hi all.

I am confused by the output when differentiating logs.

When I try to differentiate 6(e^x)lny wrt x, using : D[6 e^x ln[y], x], the output is 6 e^x ln[y] Log[e].
The answer should be 6(e^x)lny.
When I try to differentiate D[6 e^ln[u cos[v]] ln[u sin[v]], u], the output is 6 e^ln[u cos[v]] cos[v] ln[u sin[v]] Log[e] Derivative[1][ln][
u cos[v]] + 6 e^ln[u cos[v]] sin[v] Derivative[1][ln][u sin[v]]
It’s all rather confusing. Can someone please explain the outputs?

Thanks in advance.

2

You need to use correct Wolfram Language syntax:

Log[] is the natural log, and E is Euler’s constant.

D[6 E^x Log[y], x]

From which you get

6 E^x Log[y]

Mathematica has very good documentation. You should read it.

3

Thank you.