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The derivative of the function/ arcsin^5(4x)log2(x-5)

Derivative of arcsin^5(4x)log2(x-5)

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

You have entered [src] 
    5      log(x - 5)
asin (4*x)*----------
             log(2)
log⁡(x−5)log⁡(2)asin⁡5(4x)\frac{\log{\left(x - 5 \right)}}{\log{\left(2 \right)}} \operatorname{asin}^{5}{\left(4 x \right)} 
asin(4*x)^5*(log(x - 5)/log(2))
The graph
02468-8-6-4-2-10100.02-0.02
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      5                 4                
  asin (4*x)     20*asin (4*x)*log(x - 5)
-------------- + ------------------------
(x - 5)*log(2)       ___________         
                    /         2          
                  \/  1 - 16*x  *log(2)
asin⁡5(4x)(x−5)log⁡(2)+20log⁡(x−5)asin⁡4(4x)1−16x2log⁡(2)\frac{\operatorname{asin}^{5}{\left(4 x \right)}}{\left(x - 5\right) \log{\left(2 \right)}} + \frac{20 \log{\left(x - 5 \right)} \operatorname{asin}^{4}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \log{\left(2 \right)}}
Simplify
The second derivative [src] 
           /      2                                                                                 \
    3      |  asin (4*x)       /      1         x*asin(4*x)  \                     40*asin(4*x)     |
asin (4*x)*|- ---------- + 320*|- ---------- + --------------|*log(-5 + x) + -----------------------|
           |          2        |           2              3/2|                  ___________         |
           |  (-5 + x)         |  -1 + 16*x    /        2\   |                 /         2          |
           \                   \               \1 - 16*x /   /               \/  1 - 16*x  *(-5 + x)/
-----------------------------------------------------------------------------------------------------
                                                log(2)
(320(xasin⁡(4x)(1−16x2)32−116x2−1)log⁡(x−5)−asin⁡2(4x)(x−5)2+40asin⁡(4x)1−16x2(x−5))asin⁡3(4x)log⁡(2)\frac{\left(320 \left(\frac{x \operatorname{asin}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{16 x^{2} - 1}\right) \log{\left(x - 5 \right)} - \frac{\operatorname{asin}^{2}{\left(4 x \right)}}{\left(x - 5\right)^{2}} + \frac{40 \operatorname{asin}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \left(x - 5\right)}\right) \operatorname{asin}^{3}{\left(4 x \right)}}{\log{\left(2 \right)}}
Simplify
The third derivative [src] 
             /                                                                                                                                    /      1         x*asin(4*x)  \          \
             |                                                                                                                                480*|- ---------- + --------------|*asin(4*x)|
             |                                                                                                                                    |           2              3/2|          |
             |    3            /                       2                               2     2     \                           2                  |  -1 + 16*x    /        2\   |          |
      2      |asin (4*x)       |      12           asin (4*x)     48*x*asin(4*x)   48*x *asin (4*x)|                    30*asin (4*x)             \               \1 - 16*x /   /          |
2*asin (4*x)*|---------- + 160*|-------------- + -------------- + -------------- + ----------------|*log(-5 + x) - ------------------------ + ---------------------------------------------|
             |        3        |           3/2              3/2               2                5/2 |                  ___________                                 -5 + x                   |
             |(-5 + x)         |/        2\      /        2\      /         2\      /        2\    |                 /         2          2                                                |
             \                 \\1 - 16*x /      \1 - 16*x /      \-1 + 16*x /      \1 - 16*x /    /               \/  1 - 16*x  *(-5 + x)                                                 /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                           log(2)
2(160(48x2asin⁡2(4x)(1−16x2)52+48xasin⁡(4x)(16x2−1)2+asin⁡2(4x)(1−16x2)32+12(1−16x2)32)log⁡(x−5)+480(xasin⁡(4x)(1−16x2)32−116x2−1)asin⁡(4x)x−5+asin⁡3(4x)(x−5)3−30asin⁡2(4x)1−16x2(x−5)2)asin⁡2(4x)log⁡(2)\frac{2 \left(160 \left(\frac{48 x^{2} \operatorname{asin}^{2}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{5}{2}}} + \frac{48 x \operatorname{asin}{\left(4 x \right)}}{\left(16 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{12}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}}\right) \log{\left(x - 5 \right)} + \frac{480 \left(\frac{x \operatorname{asin}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{16 x^{2} - 1}\right) \operatorname{asin}{\left(4 x \right)}}{x - 5} + \frac{\operatorname{asin}^{3}{\left(4 x \right)}}{\left(x - 5\right)^{3}} - \frac{30 \operatorname{asin}^{2}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \left(x - 5\right)^{2}}\right) \operatorname{asin}^{2}{\left(4 x \right)}}{\log{\left(2 \right)}}
Simplify
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