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y=x^atanx
The derivative of the function/ y=x^atanx

Derivative of y=x^atanx

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 atan(x)
x
xatan⁡(x)x^{\operatorname{atan}{\left(x \right)}} 
x^atan(x)
Detail solution

  1. Don't know the steps in finding this derivative.

    But the derivative is

    (log⁡(atan⁡(x))+1)atan⁡atan⁡(x)(x)\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)} + 1\right) \operatorname{atan}^{\operatorname{atan}{\left(x \right)}}{\left(x \right)}

The answer is:

(log⁡(atan⁡(x))+1)atan⁡atan⁡(x)(x)\left(\log{\left(\operatorname{atan}{\left(x \right)} \right)} + 1\right) \operatorname{atan}^{\operatorname{atan}{\left(x \right)}}{\left(x \right)}

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 atan(x) /atan(x)   log(x)\
x       *|------- + ------|
         |   x           2|
         \          1 + x /
xatan⁡(x)(log⁡(x)x2+1+atan⁡(x)x)x^{\operatorname{atan}{\left(x \right)}} \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right)
Simplify
The second derivative [src] 
         /                  2                                    \
 atan(x) |/atan(x)   log(x)\    atan(x)       2        2*x*log(x)|
x       *||------- + ------|  - ------- + ---------- - ----------|
         ||   x           2|        2       /     2\           2 |
         |\          1 + x /       x      x*\1 + x /   /     2\  |
         \                                             \1 + x /  /
xatan⁡(x)(−2xlog⁡(x)(x2+1)2+(log⁡(x)x2+1+atan⁡(x)x)2+2x(x2+1)−atan⁡(x)x2)x^{\operatorname{atan}{\left(x \right)}} \left(- \frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right)^{2} + \frac{2}{x \left(x^{2} + 1\right)} - \frac{\operatorname{atan}{\left(x \right)}}{x^{2}}\right)
Simplify
The third derivative [src] 
         /                  3                                                                                                                   2       \
 atan(x) |/atan(x)   log(x)\        6            3          /atan(x)   log(x)\ /atan(x)       2        2*x*log(x)\    2*log(x)   2*atan(x)   8*x *log(x)|
x       *||------- + ------|  - --------- - ----------- - 3*|------- + ------|*|------- - ---------- + ----------| - --------- + --------- + -----------|
         ||   x           2|            2    2 /     2\     |   x           2| |    2       /     2\           2 |           2        3               3 |
         |\          1 + x /    /     2\    x *\1 + x /     \          1 + x / |   x      x*\1 + x /   /     2\  |   /     2\        x        /     2\  |
         \                      \1 + x /                                       \                       \1 + x /  /   \1 + x /                 \1 + x /  /
xatan⁡(x)(8x2log⁡(x)(x2+1)3+(log⁡(x)x2+1+atan⁡(x)x)3−3(log⁡(x)x2+1+atan⁡(x)x)(2xlog⁡(x)(x2+1)2−2x(x2+1)+atan⁡(x)x2)−2log⁡(x)(x2+1)2−6(x2+1)2−3x2(x2+1)+2atan⁡(x)x3)x^{\operatorname{atan}{\left(x \right)}} \left(\frac{8 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right)^{3} - 3 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right) \left(\frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{x^{2}}\right) - \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6}{\left(x^{2} + 1\right)^{2}} - \frac{3}{x^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{atan}{\left(x \right)}}{x^{3}}\right)
Simplify
The graph
Derivative of y=x^atanx
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