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  • Identical expressions

  • (arctan(x))^ three *log2(sin(x))
  • (arc tangent of (x)) cubed multiply by logarithm of 2( sinus of (x))
  • (arc tangent of (x)) to the power of three multiply by logarithm of 2( sinus of (x))
  • (arctan(x))3*log2(sin(x))
  • arctanx3*log2sinx
  • (arctan(x))³*log2(sin(x))
  • (arctan(x)) to the power of 3*log2(sin(x))
  • (arctan(x))^3log2(sin(x))
  • (arctan(x))3log2(sin(x))
  • arctanx3log2sinx
  • arctanx^3log2sinx

  • Similar expressions

  • (arctan(x))^3*log2(sinx)
The derivative of the function/ (arctan(x))^3*log2(sin(x))

Derivative of (arctan(x))^3*log2(sin(x))

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    3    log(sin(x))
atan (x)*-----------
            log(2)
log⁡(sin⁡(x))log⁡(2)atan⁡3(x)\frac{\log{\left(\sin{\left(x \right)} \right)}}{\log{\left(2 \right)}} \operatorname{atan}^{3}{\left(x \right)} 
atan(x)^3*(log(sin(x))/log(2))
The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    3                   2               
atan (x)*cos(x)   3*atan (x)*log(sin(x))
--------------- + ----------------------
 log(2)*sin(x)       /     2\           
                     \1 + x /*log(2)
cos⁡(x)atan⁡3(x)log⁡(2)sin⁡(x)+3log⁡(sin⁡(x))atan⁡2(x)(x2+1)log⁡(2)\frac{\cos{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)}}{\log{\left(2 \right)} \sin{\left(x \right)}} + \frac{3 \log{\left(\sin{\left(x \right)} \right)} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right) \log{\left(2 \right)}}
Simplify
The second derivative [src] 
/           /       2   \                                                    \        
|      2    |    cos (x)|   6*(-1 + x*atan(x))*log(sin(x))   6*atan(x)*cos(x)|        
|- atan (x)*|1 + -------| - ------------------------------ + ----------------|*atan(x)
|           |       2   |                     2              /     2\        |        
|           \    sin (x)/             /     2\               \1 + x /*sin(x) |        
\                                     \1 + x /                               /        
--------------------------------------------------------------------------------------
                                        log(2)
(−(1+cos⁡2(x)sin⁡2(x))atan⁡2(x)+6cos⁡(x)atan⁡(x)(x2+1)sin⁡(x)−6(xatan⁡(x)−1)log⁡(sin⁡(x))(x2+1)2)atan⁡(x)log⁡(2)\frac{\left(- \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \operatorname{atan}^{2}{\left(x \right)} + \frac{6 \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right) \sin{\left(x \right)}} - \frac{6 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \log{\left(\sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}}\right) \operatorname{atan}{\left(x \right)}}{\log{\left(2 \right)}}
Simplify
The third derivative [src] 
             /       2   \     /                                     2     2   \                          /       2   \                                            
        2    |    cos (x)|     |  1          2      6*x*atan(x)   4*x *atan (x)|                     3    |    cos (x)|                                            
  9*atan (x)*|1 + -------|   6*|------ - atan (x) - ----------- + -------------|*log(sin(x))   2*atan (x)*|1 + -------|*cos(x)                                     
             |       2   |     |     2                      2              2   |                          |       2   |                                            
             \    sin (x)/     \1 + x                  1 + x          1 + x    /                          \    sin (x)/          18*(-1 + x*atan(x))*atan(x)*cos(x)
- ------------------------ + --------------------------------------------------------------- + ------------------------------- - ----------------------------------
                2                                               2                                           sin(x)                                2                
           1 + x                                        /     2\                                                                          /     2\                 
                                                        \1 + x /                                                                          \1 + x / *sin(x)         
-------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                               log(2)
2(1+cos⁡2(x)sin⁡2(x))cos⁡(x)atan⁡3(x)sin⁡(x)−9(1+cos⁡2(x)sin⁡2(x))atan⁡2(x)x2+1−18(xatan⁡(x)−1)cos⁡(x)atan⁡(x)(x2+1)2sin⁡(x)+6(4x2atan⁡2(x)x2+1−6xatan⁡(x)x2+1−atan⁡2(x)+1x2+1)log⁡(sin⁡(x))(x2+1)2log⁡(2)\frac{\frac{2 \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)}}{\sin{\left(x \right)}} - \frac{9 \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{18 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \sin{\left(x \right)}} + \frac{6 \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right) \log{\left(\sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}}}{\log{\left(2 \right)}}
Simplify
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