Mister Exam

Derivative of x^4lnx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 4       
x *log(x)
$$x^{4} \log{\left(x \right)}$$
d / 4       \
--\x *log(x)/
dx           
$$\frac{d}{d x} x^{4} \log{\left(x \right)}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. The derivative of is .

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 3      3       
x  + 4*x *log(x)
$$4 x^{3} \log{\left(x \right)} + x^{3}$$
The second derivative [src]
 2                
x *(7 + 12*log(x))
$$x^{2} \cdot \left(12 \log{\left(x \right)} + 7\right)$$
The third derivative [src]
2*x*(13 + 12*log(x))
$$2 x \left(12 \log{\left(x \right)} + 13\right)$$
The graph
Derivative of x^4lnx