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The derivative of the function/ arccos(5x)^(1/2)

Derivative of arccos(5x)^(1/2)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
  ___________
\/ acos(5*x)
acos⁡(5x)\sqrt{\operatorname{acos}{\left(5 x \right)}} 
sqrt(acos(5*x))
The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
             -5               
------------------------------
     ___________              
    /         2    ___________
2*\/  1 - 25*x  *\/ acos(5*x)
−521−25x2acos⁡(5x)- \frac{5}{2 \sqrt{1 - 25 x^{2}} \sqrt{\operatorname{acos}{\left(5 x \right)}}}
Simplify
The second derivative [src] 
   /          1                   10*x     \
25*|---------------------- - --------------|
   |/         2\                        3/2|
   |\-1 + 25*x /*acos(5*x)   /        2\   |
   \                         \1 - 25*x /   /
--------------------------------------------
                  ___________               
              4*\/ acos(5*x)
25(−10x(1−25x2)32+1(25x2−1)acos⁡(5x))4acos⁡(5x)\frac{25 \left(- \frac{10 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{\left(25 x^{2} - 1\right) \operatorname{acos}{\left(5 x \right)}}\right)}{4 \sqrt{\operatorname{acos}{\left(5 x \right)}}}
Simplify
The third derivative [src] 
     /                                                      2                              \
     |      4                      3                   300*x                  30*x         |
-125*|-------------- + ------------------------- + -------------- + -----------------------|
     |           3/2              3/2                         5/2               2          |
     |/        2\      /        2\        2        /        2\      /         2\           |
     \\1 - 25*x /      \1 - 25*x /   *acos (5*x)   \1 - 25*x /      \-1 + 25*x / *acos(5*x)/
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                                          ___________                                       
                                      8*\/ acos(5*x)
−125(300x2(1−25x2)52+30x(25x2−1)2acos⁡(5x)+4(1−25x2)32+3(1−25x2)32acos⁡2(5x))8acos⁡(5x)- \frac{125 \left(\frac{300 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{30 x}{\left(25 x^{2} - 1\right)^{2} \operatorname{acos}{\left(5 x \right)}} + \frac{4}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(5 x \right)}}\right)}{8 \sqrt{\operatorname{acos}{\left(5 x \right)}}}
Simplify
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