Hi, this should be pretty easy for the helpers out there. Find the derivative of loge pi^x

Thank you

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- May 2nd 2009, 07:58 PMslaypullingcatdifferential log problem
Hi, this should be pretty easy for the helpers out there. Find the derivative of loge pi^x

Thank you - May 2nd 2009, 08:03 PMReckoner
- May 2nd 2009, 08:08 PMslaypullingcat
thats what I ment, sorry. Can you please expand. I'm trying to teach myself this stuff. Can you show me with my questions please.

- May 2nd 2009, 08:11 PMwarmonk102
Here it is, hopefully the extra e in the log is a mistype.

d/dx (log (pi^x))

using log definition of power to move the x

d/dx [x (log (pi) )]

then taking derivative and answer is

log(pi) - May 2nd 2009, 08:13 PMReckoner
We use the chain rule:

$\displaystyle \frac d{dx}\left[\ln\pi^x\right]=\frac1{\pi^x}\cdot\frac d{dx}\left[\pi^x\right]$

$\displaystyle =\frac{(\ln\pi)\pi^x}{\pi^x}=\ln\pi$

An even easier method is to rewrite

$\displaystyle \ln\pi^x=x\ln\pi$

and use the constant multiple rule.