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.