Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 6
Derivative of x*e^x^2
Derivative of (x+4)^2*(x+1)+9
Derivative of (x+3)/(x-1)
Identical expressions
(x^ three)log2(x)*ln2
(x cubed ) logarithm of 2(x) multiply by ln2
(x to the power of three) logarithm of 2(x) multiply by ln2
(x3)log2(x)*ln2
x3log2x*ln2
(x³)log2(x)*ln2
(x to the power of 3)log2(x)*ln2
(x^3)log2(x)ln2
(x3)log2(x)ln2
x3log2xln2
x^3log2xln2

The derivative of the function/ (x^3)log2(x)*ln2

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

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

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:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = x^{3}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
    1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
    $g{\left(x \right)} = \log{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
    1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
    The result is: $3 x^{2} \log{\left(x \right)} + x^{2}$
  So, the result is: $\frac{3 x^{2} \log{\left(x \right)} + x^{2}}{\log{\left(2 \right)}}$
So, the result is: $3 x^{2} \log{\left(x \right)} + x^{2}$
Now simplify:

$x^{2} \left(3 \log{\left(x \right)} + 1\right)$

The answer is:

$x^{2} \left(3 \log{\left(x \right)} + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

/   2        2       \       
|  x      3*x *log(x)|       
|------ + -----------|*log(2)
\log(2)      log(2)  /

$$\left(\frac{3 x^{2} \log{\left(x \right)}}{\log{\left(2 \right)}} + \frac{x^{2}}{\log{\left(2 \right)}}\right) \log{\left(2 \right)}$$

Simplify

The second derivative [src]

x*(5 + 6*log(x))

$$x \left(6 \log{\left(x \right)} + 5\right)$$

Simplify

The third derivative [src]

11 + 6*log(x)

$$6 \log{\left(x \right)} + 11$$

Simplify