# Thread: Differentiating x ln(x)

1. ## Differentiating x ln(x)

a) Differentiate x ln(x). (x>0)
b)Hence, find an antiderivative of $\displaystyle\frac{x}{x^2+2}$

A basic question, but for some reason i keep getting it wrong, for part a am i doing the product rule wrong? cause i keep geting 1/x when the anwser is 1+ln(x)
For part be i forgot how to take the +1 one out to seperate.

2. Originally Posted by Dizko
a) Differentiate x ln(x). (x>0)
b)Hence, find an antiderivative of $\displaystyle\frac{x}{x^2+2}$

A basic question, but for some reason i keep getting it wrong, for part a am i doing the product rule wrong? cause i keep geting 1/x when the anwser is 1+ln(x)
For part be i forgot how to take the +1 one out to seperate.
Recall the product rule: $(fg)^{\prime}=f^{\prime}g+g^{\prime}f$

3. Originally Posted by Dizko
a) Differentiate x ln(x). (x>0)
b)Hence, find an antiderivative of $\displaystyle\frac{x}{x^2+2}$

A basic question, but for some reason i keep getting it wrong, for part a am i doing the product rule wrong? cause i keep geting 1/x when the anwser is 1+ln(x)
For part be i forgot how to take the +1 one out to seperate.
As Chris L T521 said, yes, using the product rule is correct. But we can't tell if you are using the product rule wrong if you dont' show us how you used it.
Show each detail of differentiating x ln(x).