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The derivative of the function/ arccos((9)^x)

Derivative of arccos((9)^x)

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

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from to

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The solution

You have entered [src] 
    / x\
acos\9 /
$$\operatorname{acos}{\left(9^{x} \right)}$$ 
acos(9^x)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   x         
 -9 *log(9)  
-------------
   __________
  /      2*x 
\/  1 - 9
$$- \frac{9^{x} \log{\left(9 \right)}}{\sqrt{1 - 9^{2 x}}}$$
Simplify
The second derivative [src] 
            /       2*x  \ 
  x    2    |      9     | 
-9 *log (9)*|1 + --------| 
            |         2*x| 
            \    1 - 9   / 
---------------------------
          __________       
         /      2*x        
       \/  1 - 9
$$- \frac{9^{x} \left(\frac{9^{2 x}}{1 - 9^{2 x}} + 1\right) \log{\left(9 \right)}^{2}}{\sqrt{1 - 9^{2 x}}}$$
Simplify
The third derivative [src] 
            /          4*x         2*x \ 
  x    3    |       3*9         4*9    | 
-9 *log (9)*|1 + ----------- + --------| 
            |              2        2*x| 
            |    /     2*x\    1 - 9   | 
            \    \1 - 9   /            / 
-----------------------------------------
                 __________              
                /      2*x               
              \/  1 - 9
$$- \frac{9^{x} \left(\frac{3 \cdot 9^{4 x}}{\left(1 - 9^{2 x}\right)^{2}} + \frac{4 \cdot 9^{2 x}}{1 - 9^{2 x}} + 1\right) \log{\left(9 \right)}^{3}}{\sqrt{1 - 9^{2 x}}}$$
Simplify
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