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y=tgsqrtxarcctg3(x)^5
The derivative of the function/ y=tgsqrtxarcctg3(x)^5

Derivative of y=tgsqrtxarcctg3(x)^5

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

The graph:

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The solution

You have entered [src] 
   /  ___\     243   
tan\\/ x /*acot   (x)
tan⁡(x)acot⁡243(x)\tan{\left(\sqrt{x} \right)} \operatorname{acot}^{243}{\left(x \right)} 
tan(sqrt(x))*acot(x)^243
The graph
02468-8-6-4-2-1010-3e423e42
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    243    /       2/  ___\\           242       /  ___\
acot   (x)*\1 + tan \\/ x //   243*acot   (x)*tan\\/ x /
---------------------------- - -------------------------
              ___                             2         
          2*\/ x                         1 + x
−243tan⁡(x)acot⁡242(x)x2+1+(tan⁡2(x)+1)acot⁡243(x)2x- \frac{243 \tan{\left(\sqrt{x} \right)} \operatorname{acot}^{242}{\left(x \right)}}{x^{2} + 1} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}^{243}{\left(x \right)}}{2 \sqrt{x}}
Simplify
The second derivative [src] 
           /                                                              /              /  ___\\                                \
           |                                       2    /       2/  ___\\ |   1     2*tan\\/ x /|                                |
           |                                   acot (x)*\1 + tan \\/ x //*|- ---- + ------------|                                |
           |                         /  ___\                              |   3/2        x      |       /       2/  ___\\        |
    241    |486*(121 + x*acot(x))*tan\\/ x /                              \  x                  /   243*\1 + tan \\/ x //*acot(x)|
acot   (x)*|-------------------------------- + -------------------------------------------------- - -----------------------------|
           |                   2                                       4                                      ___ /     2\       |
           |           /     2\                                                                             \/ x *\1 + x /       |
           \           \1 + x /                                                                                                  /
((2tan⁡(x)x−1x32)(tan⁡2(x)+1)acot⁡2(x)4+486(xacot⁡(x)+121)tan⁡(x)(x2+1)2−243(tan⁡2(x)+1)acot⁡(x)x(x2+1))acot⁡241(x)\left(\frac{\left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}{4} + \frac{486 \left(x \operatorname{acot}{\left(x \right)} + 121\right) \tan{\left(\sqrt{x} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{243 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)}\right) \operatorname{acot}^{241}{\left(x \right)}
Simplify
The third derivative [src] 
           /      /                         2     2                   \                                         /            /  ___\     /       2/  ___\\        2/  ___\\                                  /              /  ___\\                                                  \
           |      |      2      29161    4*x *acot (x)   726*x*acot(x)|    /  ___\       3    /       2/  ___\\ | 3     6*tan\\/ x /   2*\1 + tan \\/ x //   4*tan \\/ x /|           2    /       2/  ___\\ |   1     2*tan\\/ x /|                                                  |
           |  486*|- acot (x) + ------ + ------------- + -------------|*tan\\/ x /   acot (x)*\1 + tan \\/ x //*|---- - ------------ + ------------------- + -------------|   729*acot (x)*\1 + tan \\/ x //*|- ---- + ------------|                                                  |
           |      |                  2            2               2   |                                         | 5/2         2                 3/2                3/2    |                                  |   3/2        x      |       /       2/  ___\\                          |
    240    |      \             1 + x        1 + x           1 + x    /                                         \x           x                 x                  x       /                                  \  x                  /   729*\1 + tan \\/ x //*(121 + x*acot(x))*acot(x)|
acot   (x)*|- -------------------------------------------------------------------- + -------------------------------------------------------------------------------------- - ------------------------------------------------------ + -----------------------------------------------|
           |                                       2                                                                           8                                                                      /     2\                                                       2                |
           |                               /     2\                                                                                                                                                 4*\1 + x /                                           ___ /     2\                 |
           \                               \1 + x /                                                                                                                                                                                                    \/ x *\1 + x /                 /
((tan⁡2(x)+1)(−6tan⁡(x)x2+2(tan⁡2(x)+1)x32+4tan⁡2(x)x32+3x52)acot⁡3(x)8−729(2tan⁡(x)x−1x32)(tan⁡2(x)+1)acot⁡2(x)4(x2+1)−486(4x2acot⁡2(x)x2+1+726xacot⁡(x)x2+1−acot⁡2(x)+29161x2+1)tan⁡(x)(x2+1)2+729(xacot⁡(x)+121)(tan⁡2(x)+1)acot⁡(x)x(x2+1)2)acot⁡240(x)\left(\frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \left(- \frac{6 \tan{\left(\sqrt{x} \right)}}{x^{2}} + \frac{2 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{x^{\frac{3}{2}}} + \frac{4 \tan^{2}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{3}{x^{\frac{5}{2}}}\right) \operatorname{acot}^{3}{\left(x \right)}}{8} - \frac{729 \left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}{4 \left(x^{2} + 1\right)} - \frac{486 \left(\frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{726 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \operatorname{acot}^{2}{\left(x \right)} + \frac{29161}{x^{2} + 1}\right) \tan{\left(\sqrt{x} \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{729 \left(x \operatorname{acot}{\left(x \right)} + 121\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)^{2}}\right) \operatorname{acot}^{240}{\left(x \right)}
Simplify
The graph
Derivative of y=tgsqrtxarcctg3(x)^5
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