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Derivative of (x^3)log2(x)*ln2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 3 log(x)       
x *------*log(2)
   log(2)       
$$x^{3} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}} \log{\left(2 \right)}$$
(x^3*(log(x)/log(2)))*log(2)
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the product rule:

        ; to find :

        1. Apply the power rule: goes to

        ; to find :

        1. The derivative of is .

        The result is:

      So, the result is:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
/   2        2       \       
|  x      3*x *log(x)|       
|------ + -----------|*log(2)
\log(2)      log(2)  /       
$$\left(\frac{3 x^{2} \log{\left(x \right)}}{\log{\left(2 \right)}} + \frac{x^{2}}{\log{\left(2 \right)}}\right) \log{\left(2 \right)}$$
The second derivative [src]
x*(5 + 6*log(x))
$$x \left(6 \log{\left(x \right)} + 5\right)$$
The third derivative [src]
11 + 6*log(x)
$$6 \log{\left(x \right)} + 11$$