Detail solution
-
Apply the quotient rule, which is:
and .
To find :
-
Apply the power rule: goes to
To find :
-
The derivative of is .
Now plug in to the quotient rule:
-
Now simplify:
The answer is:
The first derivative
[src]
x 2*x
- ------- + ------
2 log(x)
log (x)
$$\frac{2 x}{\log{\left(x \right)}} - \frac{x}{\log{\left(x \right)}^{2}}$$
The second derivative
[src]
2
1 + ------
4 log(x)
2 - ------ + ----------
log(x) log(x)
-----------------------
log(x)
$$\frac{\frac{1 + \frac{2}{\log{\left(x \right)}}}{\log{\left(x \right)}} + 2 - \frac{4}{\log{\left(x \right)}}}{\log{\left(x \right)}}$$
The third derivative
[src]
/ 3 3 \
2*|-1 - ------- + ------|
| 2 log(x)|
\ log (x) /
-------------------------
2
x*log (x)
$$\frac{2 \left(-1 + \frac{3}{\log{\left(x \right)}} - \frac{3}{\log{\left(x \right)}^{2}}\right)}{x \log{\left(x \right)}^{2}}$$