seemingly simple derivative

**makieru** · October 17th 2009, 05:51 PM

hello all. my friend has asked me for help on a derivation but i've come up blank.

the derivation in question is:

$\frac{d}{dx}lnx^{lnx}$

i thought $lnx$

he thought $2\frac{lnx}{x}$

what do YOU think?

**redsoxfan325** · October 17th 2009, 06:05 PM

Originally Posted by makieru

hello all. my friend has asked me for help on a derivation but i've come up blank.

the derivation in question is:

$\frac{d}{dx}lnx^{lnx}$

i thought $lnx$

he thought $2\frac{lnx}{x}$

what do YOU think?

It's $\frac{2\ln x}{x}$ . Here's why:

$\ln\left(x^{\ln x}\right)=(\ln x)(\ln x)=(\ln x)^2$

Use the chain rule:

$2\ln x\cdot\frac{1}{x}=\frac{2\ln x}{x}$

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