derivation using derivative rules

Question

what is the derivative

ln|x^2/2|

my answer: we have two function ln|| and X^2. we use derivative of function outside multiply by derivative of function inside so

= 1/(X^2/2). X^2/2 . x ANS = X. the correct ans is 2/X. How come?

Our function is $2\ln(|x|)-\ln 2$. I cannot read what is written above, but your method gives $\frac{x}{x^2/2}$, which is $\frac{2}{x}$. — André Nicolas, Mar 31 '14 at 05:34

Kaj Hansen · Answer 1 · 2014-03-31T05:42:04.047

1

Use the chain rule:

$f(x) = ln(x)$

$g(x) = \frac{x^2}{2}$

So find the derivative of $y = f(g(x))$ with respect to x.

edited Mar 31 '14 at 05:42

answered Mar 31 '14 at 05:35

Kaj Hansen

I'm using the chain rule but somewhere Im making a mistake – cash Mar 31 '14 at 05:43

score 0 · Answer 2 · answered Mar 31 '14 at 05:53

0

You wrote $\dfrac{1}{x^2/2} \cdot \dfrac{x^2}{2} \cdot x$

The middle $\dfrac{x^2}{2}$ should not be there.

answered Mar 31 '14 at 05:53

Henry

2 Answers2