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y=tg(x/3)-ctg2x+arcsin5x
The derivative of the function/ y=tg(x/3)-ctg2x+arcsin5x

Derivative of y=tg(x/3)-ctg2x+arcsin5x

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

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The solution

You have entered [src] 
   /x\                       
tan|-| - cot(2*x) + asin(5*x)
   \3/
(tan⁡(x3)−cot⁡(2x))+asin⁡(5x)\left(\tan{\left(\frac{x}{3} \right)} - \cot{\left(2 x \right)}\right) + \operatorname{asin}{\left(5 x \right)} 
tan(x/3) - cot(2*x) + asin(5*x)
The graph
02468-8-6-4-2-1010-50100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                                      2/x\
                                   tan |-|
7        2              5              \3/
- + 2*cot (2*x) + -------------- + -------
3                    ___________      3   
                    /         2           
                  \/  1 - 25*x
tan⁡2(x3)3+2cot⁡2(2x)+73+51−25x2\frac{\tan^{2}{\left(\frac{x}{3} \right)}}{3} + 2 \cot^{2}{\left(2 x \right)} + \frac{7}{3} + \frac{5}{\sqrt{1 - 25 x^{2}}}
Simplify
The second derivative [src] 
                                                  /       2/x\\    /x\
                                                2*|1 + tan |-||*tan|-|
    /       2     \                125*x          \        \3//    \3/
- 8*\1 + cot (2*x)/*cot(2*x) + -------------- + ----------------------
                                          3/2             9           
                               /        2\                            
                               \1 - 25*x /
125x(1−25x2)32+2(tan⁡2(x3)+1)tan⁡(x3)9−8(cot⁡2(2x)+1)cot⁡(2x)\frac{125 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{2 \left(\tan^{2}{\left(\frac{x}{3} \right)} + 1\right) \tan{\left(\frac{x}{3} \right)}}{9} - 8 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot{\left(2 x \right)}
Simplify
The third derivative [src] 
                                                      2                                                                          
                                         /       2/x\\                                                         2/x\ /       2/x\\
                  2                    2*|1 + tan |-||                                            2       4*tan |-|*|1 + tan |-||
   /       2     \         125           \        \3//          2      /       2     \      9375*x              \3/ \        \3//
16*\1 + cot (2*x)/  + -------------- + ---------------- + 32*cot (2*x)*\1 + cot (2*x)/ + -------------- + -----------------------
                                 3/2          27                                                    5/2              27          
                      /        2\                                                        /        2\                             
                      \1 - 25*x /                                                        \1 - 25*x /
9375x2(1−25x2)52+2(tan⁡2(x3)+1)227+4(tan⁡2(x3)+1)tan⁡2(x3)27+16(cot⁡2(2x)+1)2+32(cot⁡2(2x)+1)cot⁡2(2x)+125(1−25x2)32\frac{9375 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{2 \left(\tan^{2}{\left(\frac{x}{3} \right)} + 1\right)^{2}}{27} + \frac{4 \left(\tan^{2}{\left(\frac{x}{3} \right)} + 1\right) \tan^{2}{\left(\frac{x}{3} \right)}}{27} + 16 \left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} + 32 \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot^{2}{\left(2 x \right)} + \frac{125}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}
Simplify
The graph
Derivative of y=tg(x/3)-ctg2x+arcsin5x
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