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y=5x^2×arccos2x^5

Derivada de y=5x^2×arccos2x^5

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
   2     5     
5*x *acos (2*x)
$$5 x^{2} \operatorname{acos}^{5}{\left(2 x \right)}$$
(5*x^2)*acos(2*x)^5
Gráfica
Primera derivada [src]
                      2     4     
         5        50*x *acos (2*x)
10*x*acos (2*x) - ----------------
                      __________  
                     /        2   
                   \/  1 - 4*x    
$$- \frac{50 x^{2} \operatorname{acos}^{4}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}} + 10 x \operatorname{acos}^{5}{\left(2 x \right)}$$
Segunda derivada [src]
       3      /    2            2 /    2        x*acos(2*x) \   20*x*acos(2*x)\
10*acos (2*x)*|acos (2*x) - 20*x *|--------- + -------------| - --------------|
              |                   |        2             3/2|      __________ |
              |                   |-1 + 4*x    /       2\   |     /        2  |
              \                   \            \1 - 4*x /   /   \/  1 - 4*x   /
$$10 \left(- 20 x^{2} \left(\frac{x \operatorname{acos}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{4 x^{2} - 1}\right) - \frac{20 x \operatorname{acos}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}} + \operatorname{acos}^{2}{\left(2 x \right)}\right) \operatorname{acos}^{3}{\left(2 x \right)}$$
Tercera derivada [src]
                /     /                      2                              2     2     \          2                                                  \
         2      |   2 |      12          acos (2*x)    24*x*acos(2*x)   12*x *acos (2*x)|    3*acos (2*x)        /    2        x*acos(2*x) \          |
-100*acos (2*x)*|2*x *|------------- + ------------- - -------------- + ----------------| + ------------- + 12*x*|--------- + -------------|*acos(2*x)|
                |     |          3/2             3/2               2               5/2  |      __________        |        2             3/2|          |
                |     |/       2\      /       2\       /        2\      /       2\     |     /        2         |-1 + 4*x    /       2\   |          |
                \     \\1 - 4*x /      \1 - 4*x /       \-1 + 4*x /      \1 - 4*x /     /   \/  1 - 4*x          \            \1 - 4*x /   /          /
$$- 100 \left(2 x^{2} \left(\frac{12 x^{2} \operatorname{acos}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} - \frac{24 x \operatorname{acos}{\left(2 x \right)}}{\left(4 x^{2} - 1\right)^{2}} + \frac{\operatorname{acos}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{12}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right) + 12 x \left(\frac{x \operatorname{acos}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{4 x^{2} - 1}\right) \operatorname{acos}{\left(2 x \right)} + \frac{3 \operatorname{acos}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}\right) \operatorname{acos}^{2}{\left(2 x \right)}$$
Gráfico
Derivada de y=5x^2×arccos2x^5