Mister Exam

Derivative of y=xln²x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
     2   
x*log (x)
$$x \log{\left(x \right)}^{2}$$
d /     2   \
--\x*log (x)/
dx           
$$\frac{d}{d x} x \log{\left(x \right)}^{2}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of is .

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   2              
log (x) + 2*log(x)
$$\log{\left(x \right)}^{2} + 2 \log{\left(x \right)}$$
The second derivative [src]
2*(1 + log(x))
--------------
      x       
$$\frac{2 \left(\log{\left(x \right)} + 1\right)}{x}$$
The third derivative [src]
-2*log(x)
---------
     2   
    x    
$$- \frac{2 \log{\left(x \right)}}{x^{2}}$$
The graph
Derivative of y=xln²x