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x^tgx*arctgx^2
The derivative of the function/ x^tgx*arctgx^2

Derivative of x^tgx*arctgx^2

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

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The solution

You have entered [src] 
 tan(x)     2   
x      *acot (x)
xtan⁡(x)acot⁡2(x)x^{\tan{\left(x \right)}} \operatorname{acot}^{2}{\left(x \right)} 
d / tan(x)     2   \
--\x      *acot (x)/
dx
ddxxtan⁡(x)acot⁡2(x)\frac{d}{d x} x^{\tan{\left(x \right)}} \operatorname{acot}^{2}{\left(x \right)}
Transform
The graph
02468-8-6-4-2-10105000000000000-2500000000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                                                      tan(x)        
 tan(x)     2    /tan(x)   /       2   \       \   2*x      *acot(x)
x      *acot (x)*|------ + \1 + tan (x)/*log(x)| - -----------------
                 \  x                          /              2     
                                                         1 + x
xtan⁡(x)((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)acot⁡2(x)−2xtan⁡(x)acot⁡(x)x2+1x^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \operatorname{acot}^{2}{\left(x \right)} - \frac{2 x^{\tan{\left(x \right)}} \operatorname{acot}{\left(x \right)}}{x^{2} + 1}
Simplify
The second derivative [src] 
        /                                                                                                                                 /tan(x)   /       2   \       \        \
        |         /                               2              /       2   \                                \                         4*|------ + \1 + tan (x)/*log(x)|*acot(x)|
 tan(x) |    2    |/tan(x)   /       2   \       \    tan(x)   2*\1 + tan (x)/     /       2   \              |   2*(1 + 2*x*acot(x))     \  x                          /        |
x      *|acot (x)*||------ + \1 + tan (x)/*log(x)|  - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| + ------------------- - -----------------------------------------|
        |         |\  x                          /       2            x                                       |                2                               2                 |
        |         \                                     x                                                     /        /     2\                           1 + x                  |
        \                                                                                                              \1 + x /                                                  /
xtan⁡(x)((((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)2+2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)acot⁡2(x)−4((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)acot⁡(x)x2+1+2⋅(2xacot⁡(x)+1)(x2+1)2)x^{\tan{\left(x \right)}} \left(\left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) \operatorname{acot}^{2}{\left(x \right)} - \frac{4 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{2 \cdot \left(2 x \operatorname{acot}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}}\right)
Simplify
The third derivative [src] 
        /                                                                                                                                                                                                                                                                  /                       2        \     /                               2              /       2   \                                \                                                              \
        |                                                                                                                                                                                                                                                                  |            3*x     4*x *acot(x)|     |/tan(x)   /       2   \       \    tan(x)   2*\1 + tan (x)/     /       2   \              |                                                              |
        |                                                                                                                                                                                                                                                                4*|-acot(x) + ------ + ------------|   6*||------ + \1 + tan (x)/*log(x)|  - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|*acot(x)                       /tan(x)   /       2   \       \|
        |         /                               3     /       2   \                             2                                            /             /       2   \                                \                                      /       2   \       \     |                2           2   |     |\  x                          /       2            x                                       |           6*(1 + 2*x*acot(x))*|------ + \1 + tan (x)/*log(x)||
 tan(x) |    2    |/tan(x)   /       2   \       \    3*\1 + tan (x)/   2*tan(x)     /       2   \             /tan(x)   /       2   \       \ |  tan(x)   2*\1 + tan (x)/     /       2   \              |        2    /       2   \          6*\1 + tan (x)/*tan(x)|     \           1 + x       1 + x    /     \                                     x                                                     /                               \  x                          /|
x      *|acot (x)*||------ + \1 + tan (x)/*log(x)|  - --------------- + -------- + 2*\1 + tan (x)/ *log(x) + 3*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| + 4*tan (x)*\1 + tan (x)/*log(x) + ----------------------| - ------------------------------------ - ------------------------------------------------------------------------------------------------------- + ---------------------------------------------------|
        |         |\  x                          /            2             3                                  \  x                          / |     2            x                                       |                                              x           |                        2                                                                       2                                                                                2                     |
        |         \                                          x             x                                                                   \    x                                                     /                                                          /                /     2\                                                                   1 + x                                                                         /     2\                      |
        \                                                                                                                                                                                                                                                                             \1 + x /                                                                                                                                                 \1 + x /                      /
xtan⁡(x)((((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)3+3((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)(2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)+2(tan⁡2(x)+1)2log⁡(x)+4(tan⁡2(x)+1)log⁡(x)tan⁡2(x)+6(tan⁡2(x)+1)tan⁡(x)x−3(tan⁡2(x)+1)x2+2tan⁡(x)x3)acot⁡2(x)−6(((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)2+2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)acot⁡(x)x2+1+6⋅(2xacot⁡(x)+1)((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)(x2+1)2−4⋅(4x2acot⁡(x)x2+1+3xx2+1−acot⁡(x))(x2+1)2)x^{\tan{\left(x \right)}} \left(\left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} + \frac{2 \tan{\left(x \right)}}{x^{3}}\right) \operatorname{acot}^{2}{\left(x \right)} - \frac{6 \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{6 \cdot \left(2 x \operatorname{acot}{\left(x \right)} + 1\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{4 \cdot \left(\frac{4 x^{2} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}\right)
Simplify
The graph
Derivative of x^tgx*arctgx^2
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