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The derivative of the function/ 4arcsinxlnx-2/x

Derivative of 4arcsinxlnx-2/x

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

The graph:

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Piecewise:

The solution

You have entered [src] 
                   2
4*asin(x)*log(x) - -
                   x
log⁡(x)4asin⁡(x)−2x\log{\left(x \right)} 4 \operatorname{asin}{\left(x \right)} - \frac{2}{x} 
(4*asin(x))*log(x) - 2/x
The graph
02468-8-6-4-2-1010-250250
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
2    4*asin(x)     4*log(x) 
-- + --------- + -----------
 2       x          ________
x                  /      2 
                 \/  1 - x
4log⁡(x)1−x2+4asin⁡(x)x+2x2\frac{4 \log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{4 \operatorname{asin}{\left(x \right)}}{x} + \frac{2}{x^{2}}
Simplify
The second derivative [src] 
  /  1    asin(x)         2           x*log(x) \
4*|- -- - ------- + ------------- + -----------|
  |   3       2          ________           3/2|
  |  x       x          /      2    /     2\   |
  \                 x*\/  1 - x     \1 - x /   /
4(xlog⁡(x)(1−x2)32+2x1−x2−asin⁡(x)x2−1x3)4 \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{asin}{\left(x \right)}}{x^{2}} - \frac{1}{x^{3}}\right)
Simplify
The third derivative [src] 
  /                                                                 2       \
  |3         3           log(x)           3          2*asin(x)   3*x *log(x)|
4*|-- + ----------- + ----------- - -------------- + --------- + -----------|
  | 4           3/2           3/2         ________        3              5/2|
  |x    /     2\      /     2\       2   /      2        x       /     2\   |
  \     \1 - x /      \1 - x /      x *\/  1 - x                 \1 - x /   /
4(3x2log⁡(x)(1−x2)52+log⁡(x)(1−x2)32+3(1−x2)32−3x21−x2+2asin⁡(x)x3+3x4)4 \left(\frac{3 x^{2} \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{\log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \operatorname{asin}{\left(x \right)}}{x^{3}} + \frac{3}{x^{4}}\right)
Simplify
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