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  • Derivada de:
  • Derivada de e^3 Derivada de e^3
  • Derivada de x!
  • Derivada de e^x*x^3 Derivada de e^x*x^3
  • Derivada de e^x-e^-x Derivada de e^x-e^-x

  • Expresiones idénticas

  • y= dos /((a^ dos -b^ dos)^ uno / dos)*arctg(((a-b)/(a+b))^ uno / dos *(tgx/ dos))
  • y es igual a 2 dividir por ((a al cuadrado menos b al cuadrado ) en el grado 1 dividir por 2) multiplicar por arctg(((a menos b) dividir por (a más b)) en el grado 1 dividir por 2 multiplicar por (tgx dividir por 2))
  • y es igual a dos dividir por ((a en el grado dos menos b en el grado dos) en el grado uno dividir por dos) multiplicar por arctg(((a menos b) dividir por (a más b)) en el grado uno dividir por dos multiplicar por (tgx dividir por dos))
  • y=2/((a2-b2)1/2)*arctg(((a-b)/(a+b))1/2*(tgx/2))
  • y=2/a2-b21/2*arctga-b/a+b1/2*tgx/2
  • y=2/((a²-b²)^1/2)*arctg(((a-b)/(a+b))^1/2*(tgx/2))
  • y=2/((a en el grado 2-b en el grado 2) en el grado 1/2)*arctg(((a-b)/(a+b)) en el grado 1/2*(tgx/2))
  • y=2/((a^2-b^2)^1/2)arctg(((a-b)/(a+b))^1/2(tgx/2))
  • y=2/((a2-b2)1/2)arctg(((a-b)/(a+b))1/2(tgx/2))
  • y=2/a2-b21/2arctga-b/a+b1/2tgx/2
  • y=2/a^2-b^2^1/2arctga-b/a+b^1/2tgx/2
  • y=2 dividir por ((a^2-b^2)^1 dividir por 2)*arctg(((a-b) dividir por (a+b))^1 dividir por 2*(tgx dividir por 2))

  • Expresiones semejantes

  • y=2/((a^2+b^2)^1/2)*arctg(((a-b)/(a+b))^1/2*(tgx/2))
  • y=2/((a^2-b^2)^1/2)*arctg(((a-b)/(a-b))^1/2*(tgx/2))
  • y=2/((a^2-b^2)^1/2)*arctg(((a+b)/(a+b))^1/2*(tgx/2))

  • Expresiones con funciones

  • arctg
  • arctg^2(1/x)
Derivada de la función/ y=2/((a^2-b^2)^1/2)*arctg(((a-b)/(a+b))^1/2*(tgx/2))

Derivada de y=2/((a^2-b^2)^1/2)*arctg(((a-b)/(a+b))^1/2*(tgx/2))

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
                 /    _______       \
     2           |   / a - b  tan(x)|
------------*atan|  /  ----- *------|
   _________     \\/   a + b    2   /
  /  2    2                          
\/  a  - b
2a2−b2atan⁡(tan⁡(x)2a−ba+b)\frac{2}{\sqrt{a^{2} - b^{2}}} \operatorname{atan}{\left(\frac{\tan{\left(x \right)}}{2} \sqrt{\frac{a - b}{a + b}} \right)} 
(2/sqrt(a^2 - b^2))*atan(sqrt((a - b)/(a + b))*(tan(x)/2))
Primera derivada [src] 
         _______ /       2   \    
        / a - b  |1   tan (x)|    
   2*  /  ----- *|- + -------|    
     \/   a + b  \2      2   /    
----------------------------------
/       2           \    _________
|    tan (x)*(a - b)|   /  2    2 
|1 + ---------------|*\/  a  - b  
\       4*(a + b)   /
2a−ba+b(tan⁡2(x)2+12)a2−b2((a−b)tan⁡2(x)4(a+b)+1)\frac{2 \sqrt{\frac{a - b}{a + b}} \left(\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}\right)}{\sqrt{a^{2} - b^{2}} \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{4 \left(a + b\right)} + 1\right)}
Simplificar
Segunda derivada [src] 
       _______               /         /       2   \            \       
      / a - b  /       2   \ |         \1 + tan (x)/*(a - b)    |       
-8*  /  ----- *\1 + tan (x)/*|-1 + -----------------------------|*tan(x)
   \/   a + b                |     /       2           \        |       
                             |     |    tan (x)*(a - b)|        |       
                             |     |4 + ---------------|*(a + b)|       
                             \     \         a + b     /        /       
------------------------------------------------------------------------
                   /       2           \    _________                   
                   |    tan (x)*(a - b)|   /  2    2                    
                   |4 + ---------------|*\/  a  - b                     
                   \         a + b     /
−8a−ba+b((a−b)(tan⁡2(x)+1)(a+b)((a−b)tan⁡2(x)a+b+4)−1)(tan⁡2(x)+1)tan⁡(x)a2−b2((a−b)tan⁡2(x)a+b+4)- \frac{8 \sqrt{\frac{a - b}{a + b}} \left(\frac{\left(a - b\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(a + b\right) \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{a + b} + 4\right)} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\sqrt{a^{2} - b^{2}} \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{a + b} + 4\right)}
Simplificar
3-я производная [src] 
                            /                                 2                                                               2                 \
      _______               |                    /       2   \                    2    /       2   \             /       2   \         2    2   |
     / a - b  /       2   \ |         2          \1 + tan (x)/ *(a - b)      6*tan (x)*\1 + tan (x)/*(a - b)   4*\1 + tan (x)/ *(a - b) *tan (x)|
8*  /  ----- *\1 + tan (x)/*|1 + 3*tan (x) - ----------------------------- - ------------------------------- + ---------------------------------|
  \/   a + b                |                /       2           \            /       2           \                                  2          |
                            |                |    tan (x)*(a - b)|            |    tan (x)*(a - b)|             /       2           \           |
                            |                |4 + ---------------|*(a + b)    |4 + ---------------|*(a + b)     |    tan (x)*(a - b)|         2 |
                            |                \         a + b     /            \         a + b     /             |4 + ---------------| *(a + b)  |
                            \                                                                                   \         a + b     /           /
-------------------------------------------------------------------------------------------------------------------------------------------------
                                                        /       2           \    _________                                                       
                                                        |    tan (x)*(a - b)|   /  2    2                                                        
                                                        |4 + ---------------|*\/  a  - b                                                         
                                                        \         a + b     /
8a−ba+b(tan⁡2(x)+1)(4(a−b)2(tan⁡2(x)+1)2tan⁡2(x)(a+b)2((a−b)tan⁡2(x)a+b+4)2−(a−b)(tan⁡2(x)+1)2(a+b)((a−b)tan⁡2(x)a+b+4)−6(a−b)(tan⁡2(x)+1)tan⁡2(x)(a+b)((a−b)tan⁡2(x)a+b+4)+3tan⁡2(x)+1)a2−b2((a−b)tan⁡2(x)a+b+4)\frac{8 \sqrt{\frac{a - b}{a + b}} \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{4 \left(a - b\right)^{2} \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{2}{\left(x \right)}}{\left(a + b\right)^{2} \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{a + b} + 4\right)^{2}} - \frac{\left(a - b\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\left(a + b\right) \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{a + b} + 4\right)} - \frac{6 \left(a - b\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{\left(a + b\right) \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{a + b} + 4\right)} + 3 \tan^{2}{\left(x \right)} + 1\right)}{\sqrt{a^{2} - b^{2}} \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{a + b} + 4\right)}
Simplificar
Tercera derivada [src] 
                            /                                 2                                                               2                 \
      _______               |                    /       2   \                    2    /       2   \             /       2   \         2    2   |
     / a - b  /       2   \ |         2          \1 + tan (x)/ *(a - b)      6*tan (x)*\1 + tan (x)/*(a - b)   4*\1 + tan (x)/ *(a - b) *tan (x)|
8*  /  ----- *\1 + tan (x)/*|1 + 3*tan (x) - ----------------------------- - ------------------------------- + ---------------------------------|
  \/   a + b                |                /       2           \            /       2           \                                  2          |
                            |                |    tan (x)*(a - b)|            |    tan (x)*(a - b)|             /       2           \           |
                            |                |4 + ---------------|*(a + b)    |4 + ---------------|*(a + b)     |    tan (x)*(a - b)|         2 |
                            |                \         a + b     /            \         a + b     /             |4 + ---------------| *(a + b)  |
                            \                                                                                   \         a + b     /           /
-------------------------------------------------------------------------------------------------------------------------------------------------
                                                        /       2           \    _________                                                       
                                                        |    tan (x)*(a - b)|   /  2    2                                                        
                                                        |4 + ---------------|*\/  a  - b                                                         
                                                        \         a + b     /
8a−ba+b(tan⁡2(x)+1)(4(a−b)2(tan⁡2(x)+1)2tan⁡2(x)(a+b)2((a−b)tan⁡2(x)a+b+4)2−(a−b)(tan⁡2(x)+1)2(a+b)((a−b)tan⁡2(x)a+b+4)−6(a−b)(tan⁡2(x)+1)tan⁡2(x)(a+b)((a−b)tan⁡2(x)a+b+4)+3tan⁡2(x)+1)a2−b2((a−b)tan⁡2(x)a+b+4)\frac{8 \sqrt{\frac{a - b}{a + b}} \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{4 \left(a - b\right)^{2} \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan^{2}{\left(x \right)}}{\left(a + b\right)^{2} \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{a + b} + 4\right)^{2}} - \frac{\left(a - b\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\left(a + b\right) \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{a + b} + 4\right)} - \frac{6 \left(a - b\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{\left(a + b\right) \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{a + b} + 4\right)} + 3 \tan^{2}{\left(x \right)} + 1\right)}{\sqrt{a^{2} - b^{2}} \left(\frac{\left(a - b\right) \tan^{2}{\left(x \right)}}{a + b} + 4\right)}
Simplificar
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