derivative of xlnx-x

Question

zepp · Answer

Separate it into two derivatives and use the product rule :D

campbell_st · Answer

well you need to product rule for xln(x) 
and -x is differentiated in the normal fashion

zepp · Answer

$$\large \frac{d}{dx}x\ln (x)-\frac{d}{dx}x$$

anonymous · Answer

thats where i get stuck. I have f'(x)=lnx+x(1/x)-1 

What's next?

campbell_st · Answer

ok... all you need to do is multiply x by 1/x

zepp · Answer

$$\large \frac{d}{dx}x\ln(x)=(\frac{d}{dx}x)\ln(x)+x(\frac{d}{dx}\ln(x))=\ln(x)+x\frac{1}{x}=\ln(x)$$

zepp · Answer

The $\large x(\frac{1}{x})$ part could be simplied as 1, since $\LARGE x\frac{1}{x}=\frac{x}{x}=1$

zepp · Answer

And you'll get $\large f'(x)=\ln(x)+1-1$, which is simply $\large f'(x)=\ln(x)$

zepp · Answer

***I forgot a 1 here, sorry about that***$$\large \frac{d}{dx}x\ln(x)=(\frac{d}{dx}x)\ln(x)+x(\frac{d}{dx}\ln(x))=\ln(x)+x\frac{1}{x}=\ln(x)+1$$

anonymous · Answer

You're awesome. 

Nice avatar pic btw

zepp · Answer

np and thx :)

anonymous · Answer

would the 1 be negative?  lnx-1? 

It was originally xlnx-x

zepp · Answer

Nope, the derivative of xln(x) is ln(x)+1 and the derivative of x is 1
(ln(x)+1)               -             (1)
Derivative of xlnx            Derivative of x

anonymous · Answer

ok. so then the answer is just ln(x)  because the +1 and -1 cancel

zepp · Answer

Yes! :D

anonymous · Answer

sweet. Thanks again!

zepp · Answer

Welcome :)