Derivative of -ln(-\Theta): Explained

[roadworx]

Hi,

I'm trying to find the derivative of -ln(-\Theta) with respect to \Theta

The answer's -\frac{1}{\Theta}

I'm not sure why though. Here's my working.

\frac{d}{d\Theta} -ln(-\Theta)

= \frac{d}{d\Theta} ln(-\frac{1}{\Theta})

= -\Theta

Can anyone explain where I'm going wrong? Thanks.

 

[Dr.D]

d(-ln(-th))/dth
= - d(ln(-th))/dth
= - (-th)^(-1) d(-th)/dth
= - (-th)^(-1) (-1)
= - (1/th)

 

[yyat]

You need to apply the chain rule. The derivative of -\frac{1}{\Theta} is \frac{1}{\Theta^2}. If you multiply this with -\Theta you get the correct answer.