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  • Identical expressions

  • acos(x)/(four *x^ two + five)
  • arc co sinus of e of ine of (x) divide by (4 multiply by x squared plus 5)
  • arc co sinus of e of ine of (x) divide by (four multiply by x to the power of two plus five)
  • acos(x)/(4*x2+5)
  • acosx/4*x2+5
  • acos(x)/(4*x²+5)
  • acos(x)/(4*x to the power of 2+5)
  • acos(x)/(4x^2+5)
  • acos(x)/(4x2+5)
  • acosx/4x2+5
  • acosx/4x^2+5
  • acos(x) divide by (4*x^2+5)

  • Similar expressions

  • acos(x)/(4*x^2-5)
  • arccos(x)/(4*x^2+5)
  • arccosx/(4*x^2+5)
The derivative of the function/ acos(x)/(4*x^2+5)

Derivative of acos(x)/(4*x^2+5)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
acos(x) 
--------
   2    
4*x  + 5
$$\frac{\operatorname{acos}{\left(x \right)}}{4 x^{2} + 5}$$ 
acos(x)/(4*x^2 + 5)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
            1              8*x*acos(x)
- ---------------------- - -----------
     ________                        2
    /      2  /   2    \   /   2    \ 
  \/  1 - x  *\4*x  + 5/   \4*x  + 5/
$$- \frac{8 x \operatorname{acos}{\left(x \right)}}{\left(4 x^{2} + 5\right)^{2}} - \frac{1}{\sqrt{1 - x^{2}} \left(4 x^{2} + 5\right)}$$
Simplify
The second derivative [src] 
                  /          2  \                                 
                  |      16*x   |                                 
                8*|-1 + --------|*acos(x)                         
                  |            2|                                 
       x          \     5 + 4*x /                    16*x         
- ----------- + ------------------------- + ----------------------
          3/2                   2              ________           
  /     2\               5 + 4*x              /      2  /       2\
  \1 - x /                                  \/  1 - x  *\5 + 4*x /
------------------------------------------------------------------
                                    2                             
                             5 + 4*x
$$\frac{\frac{16 x}{\sqrt{1 - x^{2}} \left(4 x^{2} + 5\right)} - \frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{8 \left(\frac{16 x^{2}}{4 x^{2} + 5} - 1\right) \operatorname{acos}{\left(x \right)}}{4 x^{2} + 5}}{4 x^{2} + 5}$$
Simplify
The third derivative [src] 
          2         /          2  \                                    /          2  \        
       3*x          |      16*x   |                                    |       8*x   |        
-1 + -------     24*|-1 + --------|                              384*x*|-1 + --------|*acos(x)
           2        |            2|                 2                  |            2|        
     -1 + x         \     5 + 4*x /             24*x                   \     5 + 4*x /        
------------ - ---------------------- + ---------------------- - -----------------------------
        3/2       ________                      3/2                                 2         
/     2\         /      2  /       2\   /     2\    /       2\            /       2\          
\1 - x /       \/  1 - x  *\5 + 4*x /   \1 - x /   *\5 + 4*x /            \5 + 4*x /          
----------------------------------------------------------------------------------------------
                                                  2                                           
                                           5 + 4*x
$$\frac{\frac{24 x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(4 x^{2} + 5\right)} - \frac{384 x \left(\frac{8 x^{2}}{4 x^{2} + 5} - 1\right) \operatorname{acos}{\left(x \right)}}{\left(4 x^{2} + 5\right)^{2}} - \frac{24 \left(\frac{16 x^{2}}{4 x^{2} + 5} - 1\right)}{\sqrt{1 - x^{2}} \left(4 x^{2} + 5\right)} + \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{4 x^{2} + 5}$$
Simplify
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