Производная функции/ От одной переменной/ y' = (tan(asin(x))^(5))'

Производная tan(asin(x))^(5)

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Решение

Вы ввели [src]
   5         
tan (asin(x))
tan⁡5(asin⁡(x))\tan^{5}{\left (\operatorname{asin}{\left (x \right )} \right )}
График
02468-8-6-4-2-1010-20002000
Первая производная [src]
     4          /       2         \
5*tan (asin(x))*\1 + tan (asin(x))/
-----------------------------------
               ________            
              /      2             
            \/  1 - x
5tan⁡4(asin⁡(x))−x2+1(tan⁡2(asin⁡(x))+1)\frac{5 \tan^{4}{\left (\operatorname{asin}{\left (x \right )} \right )}}{\sqrt{- x^{2} + 1}} \left(\tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )} + 1\right)
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Вторая производная [src]
                                    /    /       2         \        2                          \
     3          /       2         \ |  4*\1 + tan (asin(x))/   2*tan (asin(x))   x*tan(asin(x))|
5*tan (asin(x))*\1 + tan (asin(x))/*|- --------------------- - --------------- + --------------|
                                    |               2                    2                3/2  |
                                    |         -1 + x               -1 + x         /     2\     |
                                    \                                             \1 - x /     /
5(tan⁡2(asin⁡(x))+1)(xtan⁡(asin⁡(x))(−x2+1)32−1x2−1(4tan⁡2(asin⁡(x))+4)−2x2−1tan⁡2(asin⁡(x)))tan⁡3(asin⁡(x))5 \left(\tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )} + 1\right) \left(\frac{x \tan{\left (\operatorname{asin}{\left (x \right )} \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1} \left(4 \tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )} + 4\right) - \frac{2}{x^{2} - 1} \tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )}\right) \tan^{3}{\left (\operatorname{asin}{\left (x \right )} \right )}
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Третья производная [src]
                                    /                                                        2                                                                                                                        \
                                    |   2                 4               /       2         \       2    2                   3                  2          /       2         \        /       2         \             |
     2          /       2         \ |tan (asin(x))   4*tan (asin(x))   12*\1 + tan (asin(x))/    3*x *tan (asin(x))   6*x*tan (asin(x))   26*tan (asin(x))*\1 + tan (asin(x))/   12*x*\1 + tan (asin(x))/*tan(asin(x))|
5*tan (asin(x))*\1 + tan (asin(x))/*|------------- + --------------- + ----------------------- + ------------------ + ----------------- + ------------------------------------ + -------------------------------------|
                                    |         3/2              3/2                   3/2                    5/2                    2                          3/2                                       2             |
                                    | /     2\         /     2\              /     2\               /     2\              /      2\                   /     2\                                 /      2\              |
                                    \ \1 - x /         \1 - x /              \1 - x /               \1 - x /              \-1 + x /                   \1 - x /                                 \-1 + x /              /
5(tan⁡2(asin⁡(x))+1)(3x2(−x2+1)52tan⁡2(asin⁡(x))+12x(x2−1)2(tan⁡2(asin⁡(x))+1)tan⁡(asin⁡(x))+6x(x2−1)2tan⁡3(asin⁡(x))+12(−x2+1)32(tan⁡2(asin⁡(x))+1)2+26tan⁡2(asin⁡(x))(−x2+1)32(tan⁡2(asin⁡(x))+1)+4tan⁡4(asin⁡(x))(−x2+1)32+tan⁡2(asin⁡(x))(−x2+1)32)tan⁡2(asin⁡(x))5 \left(\tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )} + 1\right) \left(\frac{3 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} \tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )} + \frac{12 x}{\left(x^{2} - 1\right)^{2}} \left(\tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )} + 1\right) \tan{\left (\operatorname{asin}{\left (x \right )} \right )} + \frac{6 x}{\left(x^{2} - 1\right)^{2}} \tan^{3}{\left (\operatorname{asin}{\left (x \right )} \right )} + \frac{12}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \left(\tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )} + 1\right)^{2} + \frac{26 \tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \left(\tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )} + 1\right) + \frac{4 \tan^{4}{\left (\operatorname{asin}{\left (x \right )} \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{\tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}\right) \tan^{2}{\left (\operatorname{asin}{\left (x \right )} \right )}
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