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  • Derivative of (x+3)/(x-2) Derivative of (x+3)/(x-2)
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  • Derivative of (x^2+1)^(1/2) Derivative of (x^2+1)^(1/2)

  • Identical expressions

  • ctg^ three (4x)*arcsin(sqrtx)
  • ctg cubed (4x) multiply by arc sinus of ( square root of x)
  • ctg to the power of three (4x) multiply by arc sinus of ( square root of x)
  • ctg^3(4x)*arcsin(√x)
  • ctg3(4x)*arcsin(sqrtx)
  • ctg34x*arcsinsqrtx
  • ctg³(4x)*arcsin(sqrtx)
  • ctg to the power of 3(4x)*arcsin(sqrtx)
  • ctg^3(4x)arcsin(sqrtx)
  • ctg3(4x)arcsin(sqrtx)
  • ctg34xarcsinsqrtx
  • ctg^34xarcsinsqrtx
The derivative of the function/ ctg^3(4x)*arcsin(sqrtx)

Derivative of ctg^3(4x)*arcsin(sqrtx)

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

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The solution

You have entered [src] 
   3          /  ___\
cot (4*x)*asin\\/ x /
$$\cot^{3}{\left(4 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)}$$ 
cot(4*x)^3*asin(sqrt(x))
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                                                    3         
   2      /            2     \     /  ___\       cot (4*x)    
cot (4*x)*\-12 - 12*cot (4*x)/*asin\\/ x / + -----------------
                                                 ___   _______
                                             2*\/ x *\/ 1 - x
$$\left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{\cot^{3}{\left(4 x \right)}}{2 \sqrt{x} \sqrt{1 - x}}$$
Simplify
The second derivative [src] 
/                                                                                    2      /1     1   \\         
|                                                      /       2     \            cot (4*x)*|- + ------||         
|   /       2     \ /         2     \     /  ___\   12*\1 + cot (4*x)/*cot(4*x)             \x   -1 + x/|         
|96*\1 + cot (4*x)/*\1 + 2*cot (4*x)/*asin\\/ x / - --------------------------- - ----------------------|*cot(4*x)
|                                                           ___   _______               ___   _______   |         
\                                                         \/ x *\/ 1 - x            4*\/ x *\/ 1 - x    /
$$\left(96 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \operatorname{asin}{\left(\sqrt{x} \right)} - \frac{\left(\frac{1}{x - 1} + \frac{1}{x}\right) \cot^{2}{\left(4 x \right)}}{4 \sqrt{x} \sqrt{1 - x}} - \frac{12 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)}}{\sqrt{x} \sqrt{1 - x}}\right) \cot{\left(4 x \right)}$$
Simplify
The third derivative [src] 
                                                                                                      3      /3        3           2     \                                                                                            
                                                                                                   cot (4*x)*|-- + --------- + ----------|        2      /       2     \ /1     1   \                                                 
                      /               2                                            \                         | 2           2   x*(-1 + x)|   9*cot (4*x)*\1 + cot (4*x)/*|- + ------|       /       2     \ /         2     \         
      /       2     \ |/       2     \         4             2      /       2     \|     /  ___\             \x    (-1 + x)              /                               \x   -1 + x/   144*\1 + cot (4*x)/*\1 + 2*cot (4*x)/*cot(4*x)
- 384*\1 + cot (4*x)/*\\1 + cot (4*x)/  + 2*cot (4*x) + 7*cot (4*x)*\1 + cot (4*x)//*asin\\/ x / + --------------------------------------- + ---------------------------------------- + ----------------------------------------------
                                                                                                                  ___   _______                            ___   _______                                 ___   _______                
                                                                                                              8*\/ x *\/ 1 - x                           \/ x *\/ 1 - x                                \/ x *\/ 1 - x
$$- 384 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(\left(\cot^{2}{\left(4 x \right)} + 1\right)^{2} + 7 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)} + 2 \cot^{4}{\left(4 x \right)}\right) \operatorname{asin}{\left(\sqrt{x} \right)} + \frac{9 \left(\frac{1}{x - 1} + \frac{1}{x}\right) \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)}}{\sqrt{x} \sqrt{1 - x}} + \frac{144 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)}}{\sqrt{x} \sqrt{1 - x}} + \frac{\left(\frac{3}{\left(x - 1\right)^{2}} + \frac{2}{x \left(x - 1\right)} + \frac{3}{x^{2}}\right) \cot^{3}{\left(4 x \right)}}{8 \sqrt{x} \sqrt{1 - x}}$$
Simplify
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