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Derivada de:
Derivada de x^-7
Derivada de i*n*x
Derivada de (x+7)^5
Derivada de 1/x^9
Expresiones idénticas
y=arctg*(sinx+cosx)/(sinx-cosx)
y es igual a arctg multiplicar por ( seno de x más coseno de x) dividir por ( seno de x menos coseno de x)
y=arctg(sinx+cosx)/(sinx-cosx)
y=arctgsinx+cosx/sinx-cosx
y=arctg*(sinx+cosx) dividir por (sinx-cosx)
Expresiones semejantes
y=arctg*(sinx+cosx)/(sinx+cosx)
y=arctg*(sinx-cosx)/(sinx-cosx)

Derivada de la función/ (sinx+cosx)/(sinx-cosx)/ y=arctg*(sinx+cosx)/(sinx-cosx)

Derivada de y=arctg*(sinx+cosx)/(sinx-cosx)

Solución

Ha introducido [src]

atan(sin(x) + cos(x))
---------------------
   sin(x) - cos(x)

\frac{\operatorname{atan}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{\sin{\left(x \right)} - \cos{\left(x \right)}}

atan(sin(x) + cos(x))/(sin(x) - cos(x))

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

             -sin(x) + cos(x)                (-cos(x) - sin(x))*atan(sin(x) + cos(x))
------------------------------------------ + ----------------------------------------
/                     2\                                                 2           
\1 + (sin(x) + cos(x)) /*(sin(x) - cos(x))              (sin(x) - cos(x))

\frac{\left(- \sin{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{atan}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}} + \frac{- \sin{\left(x \right)} + \cos{\left(x \right)}}{\left(\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)}

Simplificar

Segunda derivada [src]

                                                                            /                        2 \                  
                                                                            |    2*(-cos(x) + sin(x))  |                  
                                                                            |1 + ----------------------|*(cos(x) + sin(x))
/                       2\                                                  |                         2|                  
|    2*(cos(x) + sin(x)) |                          2*(cos(x) + sin(x))     \    1 + (cos(x) + sin(x)) /                  
|1 + --------------------|*atan(cos(x) + sin(x)) + ---------------------- - ----------------------------------------------
|                      2 |                                              2                                    2            
\    (-cos(x) + sin(x))  /                         1 + (cos(x) + sin(x))                1 + (cos(x) + sin(x))             
--------------------------------------------------------------------------------------------------------------------------
                                                     -cos(x) + sin(x)

\frac{- \frac{\left(1 + \frac{2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1}\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1} + \left(1 + \frac{2 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}\right) \operatorname{atan}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)} + \frac{2 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1}}{\sin{\left(x \right)} - \cos{\left(x \right)}}

Simplificar

Tercera derivada [src]

                        2                        2                        2                  2                                                                                                                                                        
     6*(cos(x) + sin(x))     2*(-cos(x) + sin(x))     8*(-cos(x) + sin(x)) *(cos(x) + sin(x))      /                       2\   /                       2\                                                                /                        2 \
1 - ---------------------- + ---------------------- - ----------------------------------------     |    2*(cos(x) + sin(x)) |   |    6*(cos(x) + sin(x)) |                                                              2 |    2*(-cos(x) + sin(x))  |
                         2                        2                                  2           3*|1 + --------------------|   |5 + --------------------|*(cos(x) + sin(x))*atan(cos(x) + sin(x))   3*(cos(x) + sin(x)) *|1 + ----------------------|
    1 + (cos(x) + sin(x))    1 + (cos(x) + sin(x))           /                     2\              |                      2 |   |                      2 |                                                                |                         2|
                                                             \1 + (cos(x) + sin(x)) /              \    (-cos(x) + sin(x))  /   \    (-cos(x) + sin(x))  /                                                                \    1 + (cos(x) + sin(x)) /
---------------------------------------------------------------------------------------------- - ---------------------------- - ------------------------------------------------------------------ + -------------------------------------------------
                                                         2                                                               2                                               2                              /                     2\                   2  
                                    1 + (cos(x) + sin(x))                                           1 + (cos(x) + sin(x))                              (-cos(x) + sin(x))                               \1 + (cos(x) + sin(x)) /*(-cos(x) + sin(x))

\frac{3 \left(1 + \frac{2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1}\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1\right) \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}} - \frac{3 \left(1 + \frac{2 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}\right)}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1} - \frac{\left(5 + \frac{6 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right) \operatorname{atan}{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}} + \frac{1 + \frac{2 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1} - \frac{6 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1} - \frac{8 \left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2} \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1\right)^{2}}}{\left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} + 1}

Simplificar

Gráfico

Derivada de y=arctg*(sinx+cosx)/(sinx-cosx)

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Expresiones idénticas

Expresiones semejantes

Derivada de y=arctg*(sinx+cosx)/(sinx-cosx)

Gráfico:

Definida a trozos:

Solución