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Derivada de la función/ y=log/ log(3)/ y=log(3)frac(1\cos)

Derivada de y=log(3)frac(1\cos)

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

Ha introducido [src] 
           /  1   \
log(3)*frac|------|
           \cos(x)/
log⁡(3)frac⁡(1cos⁡(x))\log{\left(3 \right)} \operatorname{frac}{\left(\frac{1}{\cos{\left(x \right)}}\right)} 
log(3)*frac(1/cos(x))
Primera derivada [src] 
/  d              \|                         
|-----(frac(xi_1))||       1   *log(3)*sin(x)
\dxi_1            /|xi_1=------              
                         cos(x)              
---------------------------------------------
                      2                      
                   cos (x)
log⁡(3)sin⁡(x)ddξ1frac⁡(ξ1)∣ξ1=1cos⁡(x)cos⁡2(x)\frac{\log{\left(3 \right)} \sin{\left(x \right)} \left. \frac{d}{d \xi_{1}} \operatorname{frac}{\left(\xi_{1}\right)} \right|_{\substack{ \xi_{1}=\frac{1}{\cos{\left(x \right)}} }}}{\cos^{2}{\left(x \right)}}
Simplificar
Segunda derivada [src] 
/        /   2              \|                                                                                         \       
|   2    |  d               ||                                                                                         |       
|sin (x)*|------(frac(xi_1))||                   2    /  d              \|                                             |       
|        |     2            ||       1      2*sin (x)*|-----(frac(xi_1))||       1                                     |       
|        \dxi_1             /|xi_1=------             \dxi_1            /|xi_1=------                                  |       
|                                  cos(x)                                      cos(x)   /  d              \|           |       
|---------------------------------------- + ----------------------------------------- + |-----(frac(xi_1))||       1   |*log(3)
|                   3                                           2                       \dxi_1            /|xi_1=------|       
\                cos (x)                                     cos (x)                                             cos(x)/       
-------------------------------------------------------------------------------------------------------------------------------
                                                             cos(x)
(2sin⁡2(x)ddξ1frac⁡(ξ1)∣ξ1=1cos⁡(x)cos⁡2(x)+sin⁡2(x)d2dξ12frac⁡(ξ1)∣ξ1=1cos⁡(x)cos⁡3(x)+ddξ1frac⁡(ξ1)∣ξ1=1cos⁡(x))log⁡(3)cos⁡(x)\frac{\left(\frac{2 \sin^{2}{\left(x \right)} \left. \frac{d}{d \xi_{1}} \operatorname{frac}{\left(\xi_{1}\right)} \right|_{\substack{ \xi_{1}=\frac{1}{\cos{\left(x \right)}} }}}{\cos^{2}{\left(x \right)}} + \frac{\sin^{2}{\left(x \right)} \left. \frac{d^{2}}{d \xi_{1}^{2}} \operatorname{frac}{\left(\xi_{1}\right)} \right|_{\substack{ \xi_{1}=\frac{1}{\cos{\left(x \right)}} }}}{\cos^{3}{\left(x \right)}} + \left. \frac{d}{d \xi_{1}} \operatorname{frac}{\left(\xi_{1}\right)} \right|_{\substack{ \xi_{1}=\frac{1}{\cos{\left(x \right)}} }}\right) \log{\left(3 \right)}}{\cos{\left(x \right)}}
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Tercera derivada [src] 
/                                      /   2              \|                      /   3              \|                        /   2              \|                                                       \              
|                                      |  d               ||                 2    |  d               ||                   2    |  d               ||                                                       |              
|                                    3*|------(frac(xi_1))||              sin (x)*|------(frac(xi_1))||              6*sin (x)*|------(frac(xi_1))||                   2    /  d              \|           |              
|                                      |     2            ||       1              |     3            ||       1                |     2            ||       1      6*sin (x)*|-----(frac(xi_1))||       1   |              
|                                      \dxi_1             /|xi_1=------           \dxi_1             /|xi_1=------             \dxi_1             /|xi_1=------             \dxi_1            /|xi_1=------|              
|  /  d              \|                                          cos(x)                                     cos(x)                                       cos(x)                                      cos(x)|              
|5*|-----(frac(xi_1))||       1    + ---------------------------------- + ---------------------------------------- + ------------------------------------------ + -----------------------------------------|*log(3)*sin(x)
|  \dxi_1            /|xi_1=------                 cos(x)                                    4                                           3                                            2                    |              
\                           cos(x)                                                        cos (x)                                     cos (x)                                      cos (x)                 /              
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                            2                                                                                                             
                                                                                                         cos (x)
(6sin⁡2(x)ddξ1frac⁡(ξ1)∣ξ1=1cos⁡(x)cos⁡2(x)+6sin⁡2(x)d2dξ12frac⁡(ξ1)∣ξ1=1cos⁡(x)cos⁡3(x)+sin⁡2(x)d3dξ13frac⁡(ξ1)∣ξ1=1cos⁡(x)cos⁡4(x)+5ddξ1frac⁡(ξ1)∣ξ1=1cos⁡(x)+3d2dξ12frac⁡(ξ1)∣ξ1=1cos⁡(x)cos⁡(x))log⁡(3)sin⁡(x)cos⁡2(x)\frac{\left(\frac{6 \sin^{2}{\left(x \right)} \left. \frac{d}{d \xi_{1}} \operatorname{frac}{\left(\xi_{1}\right)} \right|_{\substack{ \xi_{1}=\frac{1}{\cos{\left(x \right)}} }}}{\cos^{2}{\left(x \right)}} + \frac{6 \sin^{2}{\left(x \right)} \left. \frac{d^{2}}{d \xi_{1}^{2}} \operatorname{frac}{\left(\xi_{1}\right)} \right|_{\substack{ \xi_{1}=\frac{1}{\cos{\left(x \right)}} }}}{\cos^{3}{\left(x \right)}} + \frac{\sin^{2}{\left(x \right)} \left. \frac{d^{3}}{d \xi_{1}^{3}} \operatorname{frac}{\left(\xi_{1}\right)} \right|_{\substack{ \xi_{1}=\frac{1}{\cos{\left(x \right)}} }}}{\cos^{4}{\left(x \right)}} + 5 \left. \frac{d}{d \xi_{1}} \operatorname{frac}{\left(\xi_{1}\right)} \right|_{\substack{ \xi_{1}=\frac{1}{\cos{\left(x \right)}} }} + \frac{3 \left. \frac{d^{2}}{d \xi_{1}^{2}} \operatorname{frac}{\left(\xi_{1}\right)} \right|_{\substack{ \xi_{1}=\frac{1}{\cos{\left(x \right)}} }}}{\cos{\left(x \right)}}\right) \log{\left(3 \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}
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