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-((xsin7x)^3/((1-x^2)^((1/2)))+3*7(sin(7x)^2)*(1-x^2)^(1/2)*cos(7x))/(cos(6x)^2)
Derivada de la función/ -((xsin7x)^3/((1-x^2)^((1/2)))+3*7(sin(7x)^2)*(1-x^2)^(1/2)*cos(7x))/(cos(6x)^2)

Derivada de -((xsin7x)^3/((1-x^2)^((1/2)))+3*7(sin(7x)^2)*(1-x^2)^(1/2)*cos(7x))/(cos(6x)^2)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
              3                   ________         
  (x*sin(7*x))          2        /      2          
- ------------- - 21*sin (7*x)*\/  1 - x  *cos(7*x)
      ________                                     
     /      2                                      
   \/  1 - x                                       
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                        2                          
                     cos (6*x)
−(xsin⁡(7x))31−x2−1−x2⋅21sin⁡2(7x)cos⁡(7x)cos⁡2(6x)\frac{- \frac{\left(x \sin{\left(7 x \right)}\right)^{3}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}} \cdot 21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)}}{\cos^{2}{\left(6 x \right)}} 
(-(x*sin(7*x))^3/sqrt(1 - x^2) - (21*sin(7*x)^2)*sqrt(1 - x^2)*cos(7*x))/cos(6*x)^2
Gráfica
02468-8-6-4-2-1010-1000010000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
/         ________                             2     \                   ________              4    3         2    2                                        /              3                   ________         \         
|        /      2                      21*x*sin (7*x)|                  /      2     3        x *sin (7*x)   x *sin (7*x)*(3*sin(7*x) + 21*x*cos(7*x))      |  (x*sin(7*x))          2        /      2          |         
|- 294*\/  1 - x  *cos(7*x)*sin(7*x) + --------------|*cos(7*x) + 147*\/  1 - x  *sin (7*x) - ------------ - -----------------------------------------   12*|- ------------- - 21*sin (7*x)*\/  1 - x  *cos(7*x)|*sin(6*x)
|                                          ________  |                                                3/2                      ________                     |      ________                                     |         
|                                         /      2   |                                        /     2\                        /      2                      |     /      2                                      |         
\                                       \/  1 - x    /                                        \1 - x /                      \/  1 - x                       \   \/  1 - x                                       /         
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                                                                         2                                                                                                              3                                 
                                                                      cos (6*x)                                                                                                      cos (6*x)
12(−(xsin⁡(7x))31−x2−1−x2⋅21sin⁡2(7x)cos⁡(7x))sin⁡(6x)cos⁡3(6x)+−x4sin⁡3(7x)(1−x2)32−x2(21xcos⁡(7x)+3sin⁡(7x))sin⁡2(7x)1−x2+1471−x2sin⁡3(7x)+(21xsin⁡2(7x)1−x2−2941−x2sin⁡(7x)cos⁡(7x))cos⁡(7x)cos⁡2(6x)\frac{12 \left(- \frac{\left(x \sin{\left(7 x \right)}\right)^{3}}{\sqrt{1 - x^{2}}} - \sqrt{1 - x^{2}} \cdot 21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)}\right) \sin{\left(6 x \right)}}{\cos^{3}{\left(6 x \right)}} + \frac{- \frac{x^{4} \sin^{3}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{x^{2} \left(21 x \cos{\left(7 x \right)} + 3 \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 147 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} + \left(\frac{21 x \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 294 \sqrt{1 - x^{2}} \sin{\left(7 x \right)} \cos{\left(7 x \right)}\right) \cos{\left(7 x \right)}}{\cos^{2}{\left(6 x \right)}}
Simplificar
Segunda derivada [src] 
 /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           /         ________                /        ________                       \             4    2           2                                   \                                                                      \ 
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           |        /      2     2           |       /      2              x*sin(7*x)|            x *sin (7*x)   3*x *(7*x*cos(7*x) + sin(7*x))*sin(7*x)|                                                                      | 
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        24*|- 147*\/  1 - x  *sin (7*x) - 21*|- 14*\/  1 - x  *cos(7*x) + -----------|*cos(7*x) + ------------ + ---------------------------------------|*sin(6*x)*sin(7*x)                                                    | 
 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           |                                 |                               ________|                    3/2                     ________              |                                                                      | 
 |     /    2               ________                   ________              2    2                              \                          /        ________                       \           ________                         5    3           3    3                     /         2     \ /      ________             3         \            3            2    2                                        3    2                                         2                                      4    2                    |                                 |                              /      2 |            /     2\                       /      2               |                         2                                            | 
 |     | sin (7*x)         /      2     2             /      2     2        x *sin (7*x)   28*x*cos(7*x)*sin(7*x)|                   2      |       /      2              x*sin(7*x)|          /      2     2                 3*x *sin (7*x)   4*x *sin (7*x)         2      |    3*sin (6*x)| |     /      2             x *sin(7*x)|   147*x*sin (7*x)   21*x *sin (7*x)*(-2*cos(7*x) + 7*x*sin(7*x))   3*x *sin (7*x)*(7*x*cos(7*x) + sin(7*x))   6*x*sin (7*x)*(7*x*cos(7*x) + sin(7*x))   21*x *sin (7*x)*cos(7*x)      \                                 \                            \/  1 - x  /            \1 - x /                     \/  1 - x                /                     42*x *(7*x*cos(7*x) + sin(7*x))*cos(7*x)*sin(7*x)| 
-|- 21*|----------- - 98*\/  1 - x  *cos (7*x) + 98*\/  1 - x  *sin (7*x) + ------------ + ----------------------|*cos(7*x) + 147*sin (7*x)*|- 14*\/  1 - x  *cos(7*x) + -----------| - 3087*\/  1 - x  *sin (7*x)*cos(7*x) + -------------- + -------------- + 72*sin (7*x)*|1 + -----------|*|21*\/  1 - x  *cos(7*x) + -----------| + --------------- - -------------------------------------------- + ---------------------------------------- + --------------------------------------- + ------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------| 
 |     |   ________                                                                 3/2            ________      |                          |                               ________|                                                  5/2              3/2                  |        2      | |                             ________|        ________                        ________                                          3/2                                   ________                               3/2                                                                                        cos(6*x)                                                                                                      ________                   | 
 |     |  /      2                                                          /     2\              /      2       |                          |                              /      2 |                                          /     2\         /     2\                     \     cos (6*x) / |                            /      2 |       /      2                        /      2                                   /     2\                                     /      2                        /     2\                                                                                                                                                                                                        /      2                    | 
 \     \\/  1 - x                                                           \1 - x /            \/  1 - x        /                          \                            \/  1 - x  /                                          \1 - x /         \1 - x /                                       \                          \/  1 - x  /     \/  1 - x                       \/  1 - x                                    \1 - x /                                   \/  1 - x                         \1 - x /                                                                                                                                                                                                      \/  1 - x                     / 
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                                                                                                                                                                                                                                                                                                                                                                        2                                                                                                                                                                                                                                                                                                                                                                          
                                                                                                                                                                                                                                                                                                                                                                     cos (6*x)
−3x5sin⁡3(7x)(1−x2)52+21x4sin⁡2(7x)cos⁡(7x)(1−x2)32+3x3(7xcos⁡(7x)+sin⁡(7x))sin⁡2(7x)(1−x2)32+4x3sin⁡3(7x)(1−x2)32−21x2(7xsin⁡(7x)−2cos⁡(7x))sin⁡2(7x)1−x2+42x2(7xcos⁡(7x)+sin⁡(7x))sin⁡(7x)cos⁡(7x)1−x2+6x(7xcos⁡(7x)+sin⁡(7x))sin⁡2(7x)1−x2+147xsin⁡3(7x)1−x2−30871−x2sin⁡2(7x)cos⁡(7x)+72(3sin⁡2(6x)cos⁡2(6x)+1)(x3sin⁡(7x)1−x2+211−x2cos⁡(7x))sin⁡2(7x)+147(xsin⁡(7x)1−x2−141−x2cos⁡(7x))sin⁡2(7x)+24(x4sin⁡2(7x)(1−x2)32+3x2(7xcos⁡(7x)+sin⁡(7x))sin⁡(7x)1−x2−1471−x2sin⁡2(7x)−21(xsin⁡(7x)1−x2−141−x2cos⁡(7x))cos⁡(7x))sin⁡(6x)sin⁡(7x)cos⁡(6x)−21(x2sin⁡2(7x)(1−x2)32+28xsin⁡(7x)cos⁡(7x)1−x2+981−x2sin⁡2(7x)−981−x2cos⁡2(7x)+sin⁡2(7x)1−x2)cos⁡(7x)cos⁡2(6x)- \frac{\frac{3 x^{5} \sin^{3}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{21 x^{4} \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3 x^{3} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{4 x^{3} \sin^{3}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{21 x^{2} \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{42 x^{2} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{6 x \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{147 x \sin^{3}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 3087 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 72 \left(\frac{3 \sin^{2}{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} + 1\right) \left(\frac{x^{3} \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 21 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)} + 147 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)} + \frac{24 \left(\frac{x^{4} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3 x^{2} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 147 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} - 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \cos{\left(7 x \right)}\right) \sin{\left(6 x \right)} \sin{\left(7 x \right)}}{\cos{\left(6 x \right)}} - 21 \left(\frac{x^{2} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{28 x \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 98 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} - 98 \sqrt{1 - x^{2}} \cos^{2}{\left(7 x \right)} + \frac{\sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right) \cos{\left(7 x \right)}}{\cos^{2}{\left(6 x \right)}}
Simplificar
Tercera derivada [src] 
   /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        /     /    2               ________                   ________              2    2                              \                          /        ________                       \           ________                         5    3           3    3                 3            2    2                                        3    2                                         2                                      4    2                     2                                            \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  /         2     \ /      ________             3         \         \
   |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |     | sin (7*x)         /      2     2             /      2     2        x *sin (7*x)   28*x*cos(7*x)*sin(7*x)|                   2      |       /      2              x*sin(7*x)|          /      2     2                 3*x *sin (7*x)   4*x *sin (7*x)   147*x*sin (7*x)   21*x *sin (7*x)*(-2*cos(7*x) + 7*x*sin(7*x))   3*x *sin (7*x)*(7*x*cos(7*x) + sin(7*x))   6*x*sin (7*x)*(7*x*cos(7*x) + sin(7*x))   21*x *sin (7*x)*cos(7*x)   42*x *(7*x*cos(7*x) + sin(7*x))*cos(7*x)*sin(7*x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           2      |    3*sin (6*x)| |     /      2             x *sin(7*x)|         |
   |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     12*|- 21*|----------- - 98*\/  1 - x  *cos (7*x) + 98*\/  1 - x  *sin (7*x) + ------------ + ----------------------|*cos(7*x) + 147*sin (7*x)*|- 14*\/  1 - x  *cos(7*x) + -----------| - 3087*\/  1 - x  *sin (7*x)*cos(7*x) + -------------- + -------------- + --------------- - -------------------------------------------- + ---------------------------------------- + --------------------------------------- + ------------------------ + -------------------------------------------------|*sin(6*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           576*sin (7*x)*|2 + -----------|*|21*\/  1 - x  *cos(7*x) + -----------|*sin(6*x)|
   |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |     |   ________                                                                 3/2            ________      |                          |                               ________|                                                  5/2              3/2          ________                        ________                                          3/2                                   ________                               3/2                                ________                   |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |        2      | |                             ________|         |
   |    /           2               2           3    2                                        2                ________                         2                  \                  3           /    2               ________                   ________              2    2                              \                    ________                      ________                          4    3             2                                     6    3           4    3           |     |  /      2                                                          /     2\              /      2       |                          |                              /      2 |                                          /     2\         /     2\            /      2                        /      2                                   /     2\                                     /      2                        /     2\                                  /      2                    |                2    3           /         2     \ /         ________                /        ________                       \             4    2           2                                   \                /        ________                       \                         2    2                                      2    2                                            2                                         3    2                                        4    2                                     2    2                                      5    2                     3    2                     2    2                                      4    2                           2                      2                                                      3                                                                                                                \     cos (6*x) / |                            /      2 |         |
   |    |  294*x*sin (7*x)   3*x*sin (7*x)   3*x *sin (7*x)   42*cos(7*x)*sin(7*x)   294*x*cos (7*x)          /      2                      42*x *cos(7*x)*sin(7*x)|            49*sin (7*x)      | sin (7*x)         /      2     2             /      2     2        x *sin (7*x)   28*x*cos(7*x)*sin(7*x)|                   /      2     3                /      2     2                 49*x *sin (7*x)   2*sin (7*x)*(7*x*cos(7*x) + sin(7*x))   5*x *sin (7*x)   9*x *sin (7*x)      \     \\/  1 - x                                                           \1 - x /            \/  1 - x        /                          \                            \/  1 - x  /                                          \1 - x /         \1 - x /          \/  1 - x                       \/  1 - x                                    \1 - x /                                   \/  1 - x                         \1 - x /                                \/  1 - x                     /            53*x *sin (7*x)      |    3*sin (6*x)| |        /      2     2           |       /      2              x*sin(7*x)|            x *sin (7*x)   3*x *(7*x*cos(7*x) + sin(7*x))*sin(7*x)|                |       /      2              x*sin(7*x)|                     98*x *sin (7*x)*(7*x*cos(7*x) + sin(7*x))   49*x *sin (7*x)*(3*sin(7*x) + 7*x*cos(7*x))   28*x*sin (7*x)*(-2*cos(7*x) + 7*x*sin(7*x))   14*x *sin (7*x)*(-2*cos(7*x) + 7*x*sin(7*x))   3*x *sin (7*x)*(7*x*cos(7*x) + sin(7*x))   5*x *sin (7*x)*(7*x*cos(7*x) + sin(7*x))   42*x *sin (7*x)*cos(7*x)   56*x *sin (7*x)*cos(7*x)   98*x *cos (7*x)*(7*x*cos(7*x) + sin(7*x))   98*x *cos (7*x)*sin(7*x)   2058*x*sin (7*x)*cos(7*x)   196*x *(-2*cos(7*x) + 7*x*sin(7*x))*cos(7*x)*sin(7*x)   28*x *(7*x*cos(7*x) + sin(7*x))*cos(7*x)*sin(7*x)   56*x*(7*x*cos(7*x) + sin(7*x))*cos(7*x)*sin(7*x)                                   \                          \/  1 - x  /         |
-3*|- 7*|- --------------- + ------------- + -------------- + -------------------- + --------------- + 2744*\/  1 - x  *cos(7*x)*sin(7*x) + -----------------------|*cos(7*x) + ------------ + 98*|----------- - 98*\/  1 - x  *cos (7*x) + 98*\/  1 - x  *sin (7*x) + ------------ + ----------------------|*sin(7*x) + 7203*\/  1 - x  *sin (7*x) - 14406*\/  1 - x  *cos (7*x)*sin(7*x) - --------------- + ------------------------------------- + -------------- + -------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------- + 72*|1 + -----------|*|- 147*\/  1 - x  *sin (7*x) - 21*|- 14*\/  1 - x  *cos(7*x) + -----------|*cos(7*x) + ------------ + ---------------------------------------|*sin(7*x) + 343*|- 14*\/  1 - x  *cos(7*x) + -----------|*cos(7*x)*sin(7*x) - ----------------------------------------- - ------------------------------------------- - ------------------------------------------- - -------------------------------------------- + ---------------------------------------- + ---------------------------------------- + ------------------------ + ------------------------ + ----------------------------------------- + ------------------------ + ------------------------- - ----------------------------------------------------- + ------------------------------------------------- + ------------------------------------------------ + --------------------------------------------------------------------------------|
   |    |       ________              3/2             5/2            ________             ________                                                        3/2      |               ________       |   ________                                                                 3/2            ________      |                                                                                          3/2                     ________                         7/2              5/2                                                                                                                                                                                                                                                        cos(6*x)                                                                                                                                                                                                                                                                3/2        |        2      | |                                 |                               ________|                    3/2                     ________              |                |                               ________|                                       ________                                     ________                                      ________                                           3/2                                          5/2                                        3/2                                5/2                        3/2                            ________                                3/2                    ________                                  ________                                                   3/2                                           ________                                                          cos(6*x)                                    |
   |    |      /      2       /     2\        /     2\              /      2             /      2                                                 /     2\         |              /      2        |  /      2                                                          /     2\              /      2       |                                                                                  /     2\                       /      2                  /     2\         /     2\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           /     2\           \     cos (6*x) / |                                 |                              /      2 |            /     2\                       /      2               |                |                              /      2 |                                      /      2                                     /      2                                      /      2                                    /     2\                                     /     2\                                   /     2\                           /     2\                   /     2\                              /      2                         /     2\                      /      2                                  /      2                                            /     2\                                             /      2                                                                                                       |
   \    \    \/  1 - x        \1 - x /        \1 - x /            \/  1 - x            \/  1 - x                                                  \1 - x /         /            \/  1 - x         \\/  1 - x                                                           \1 - x /            \/  1 - x        /                                                                                  \1 - x /                     \/  1 - x                   \1 - x /         \1 - x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \1 - x /                             \                                 \                            \/  1 - x  /            \1 - x /                     \/  1 - x                /                \                            \/  1 - x  /                                    \/  1 - x                                    \/  1 - x                                     \/  1 - x                                     \1 - x /                                     \1 - x /                                   \1 - x /                           \1 - x /                   \1 - x /                            \/  1 - x                          \1 - x /                    \/  1 - x                                 \/  1 - x                                             \1 - x /                                           \/  1 - x                                                                                                        /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             cos (6*x)
−3(5x6sin⁡3(7x)(1−x2)72+42x5sin⁡2(7x)cos⁡(7x)(1−x2)52−49x4sin⁡3(7x)(1−x2)32+98x4sin⁡(7x)cos⁡2(7x)(1−x2)32+3x4(7xcos⁡(7x)+sin⁡(7x))sin⁡2(7x)(1−x2)52+9x4sin⁡3(7x)(1−x2)52−14x3(7xsin⁡(7x)−2cos⁡(7x))sin⁡2(7x)(1−x2)32+28x3(7xcos⁡(7x)+sin⁡(7x))sin⁡(7x)cos⁡(7x)(1−x2)32+56x3sin⁡2(7x)cos⁡(7x)(1−x2)32−196x2(7xsin⁡(7x)−2cos⁡(7x))sin⁡(7x)cos⁡(7x)1−x2−98x2(7xcos⁡(7x)+sin⁡(7x))sin⁡2(7x)1−x2+98x2(7xcos⁡(7x)+sin⁡(7x))cos⁡2(7x)1−x2−49x2(7xcos⁡(7x)+3sin⁡(7x))sin⁡2(7x)1−x2+5x2(7xcos⁡(7x)+sin⁡(7x))sin⁡2(7x)(1−x2)32+53x2sin⁡3(7x)(1−x2)32−28x(7xsin⁡(7x)−2cos⁡(7x))sin⁡2(7x)1−x2+56x(7xcos⁡(7x)+sin⁡(7x))sin⁡(7x)cos⁡(7x)1−x2+2058xsin⁡2(7x)cos⁡(7x)1−x2+72031−x2sin⁡3(7x)−144061−x2sin⁡(7x)cos⁡2(7x)+72(3sin⁡2(6x)cos⁡2(6x)+1)(x4sin⁡2(7x)(1−x2)32+3x2(7xcos⁡(7x)+sin⁡(7x))sin⁡(7x)1−x2−1471−x2sin⁡2(7x)−21(xsin⁡(7x)1−x2−141−x2cos⁡(7x))cos⁡(7x))sin⁡(7x)+576(3sin⁡2(6x)cos⁡2(6x)+2)(x3sin⁡(7x)1−x2+211−x2cos⁡(7x))sin⁡(6x)sin⁡2(7x)cos⁡(6x)+343(xsin⁡(7x)1−x2−141−x2cos⁡(7x))sin⁡(7x)cos⁡(7x)+98(x2sin⁡2(7x)(1−x2)32+28xsin⁡(7x)cos⁡(7x)1−x2+981−x2sin⁡2(7x)−981−x2cos⁡2(7x)+sin⁡2(7x)1−x2)sin⁡(7x)−7(3x3sin⁡2(7x)(1−x2)52+42x2sin⁡(7x)cos⁡(7x)(1−x2)32−294xsin⁡2(7x)1−x2+294xcos⁡2(7x)1−x2+3xsin⁡2(7x)(1−x2)32+27441−x2sin⁡(7x)cos⁡(7x)+42sin⁡(7x)cos⁡(7x)1−x2)cos⁡(7x)+12(3x5sin⁡3(7x)(1−x2)52+21x4sin⁡2(7x)cos⁡(7x)(1−x2)32+3x3(7xcos⁡(7x)+sin⁡(7x))sin⁡2(7x)(1−x2)32+4x3sin⁡3(7x)(1−x2)32−21x2(7xsin⁡(7x)−2cos⁡(7x))sin⁡2(7x)1−x2+42x2(7xcos⁡(7x)+sin⁡(7x))sin⁡(7x)cos⁡(7x)1−x2+6x(7xcos⁡(7x)+sin⁡(7x))sin⁡2(7x)1−x2+147xsin⁡3(7x)1−x2−30871−x2sin⁡2(7x)cos⁡(7x)+147(xsin⁡(7x)1−x2−141−x2cos⁡(7x))sin⁡2(7x)−21(x2sin⁡2(7x)(1−x2)32+28xsin⁡(7x)cos⁡(7x)1−x2+981−x2sin⁡2(7x)−981−x2cos⁡2(7x)+sin⁡2(7x)1−x2)cos⁡(7x))sin⁡(6x)cos⁡(6x)+2(7xcos⁡(7x)+sin⁡(7x))sin⁡2(7x)1−x2+49sin⁡3(7x)1−x2)cos⁡2(6x)- \frac{3 \left(\frac{5 x^{6} \sin^{3}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{7}{2}}} + \frac{42 x^{5} \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{49 x^{4} \sin^{3}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{98 x^{4} \sin{\left(7 x \right)} \cos^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3 x^{4} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{9 x^{4} \sin^{3}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{14 x^{3} \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{28 x^{3} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{56 x^{3} \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{196 x^{2} \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - \frac{98 x^{2} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{98 x^{2} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \cos^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - \frac{49 x^{2} \left(7 x \cos{\left(7 x \right)} + 3 \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{5 x^{2} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{53 x^{2} \sin^{3}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{28 x \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{56 x \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{2058 x \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 7203 \sqrt{1 - x^{2}} \sin^{3}{\left(7 x \right)} - 14406 \sqrt{1 - x^{2}} \sin{\left(7 x \right)} \cos^{2}{\left(7 x \right)} + 72 \left(\frac{3 \sin^{2}{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} + 1\right) \left(\frac{x^{4} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3 x^{2} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 147 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} - 21 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} + \frac{576 \left(\frac{3 \sin^{2}{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} + 2\right) \left(\frac{x^{3} \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 21 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(6 x \right)} \sin^{2}{\left(7 x \right)}}{\cos{\left(6 x \right)}} + 343 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)} + 98 \left(\frac{x^{2} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{28 x \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 98 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} - 98 \sqrt{1 - x^{2}} \cos^{2}{\left(7 x \right)} + \frac{\sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right) \sin{\left(7 x \right)} - 7 \left(\frac{3 x^{3} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{42 x^{2} \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{294 x \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{294 x \cos^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{3 x \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2744 \sqrt{1 - x^{2}} \sin{\left(7 x \right)} \cos{\left(7 x \right)} + \frac{42 \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right) \cos{\left(7 x \right)} + \frac{12 \left(\frac{3 x^{5} \sin^{3}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{21 x^{4} \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3 x^{3} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{4 x^{3} \sin^{3}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{21 x^{2} \left(7 x \sin{\left(7 x \right)} - 2 \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{42 x^{2} \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{6 x \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{147 x \sin^{3}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 3087 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} + 147 \left(\frac{x \sin{\left(7 x \right)}}{\sqrt{1 - x^{2}}} - 14 \sqrt{1 - x^{2}} \cos{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)} - 21 \left(\frac{x^{2} \sin^{2}{\left(7 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{28 x \sin{\left(7 x \right)} \cos{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + 98 \sqrt{1 - x^{2}} \sin^{2}{\left(7 x \right)} - 98 \sqrt{1 - x^{2}} \cos^{2}{\left(7 x \right)} + \frac{\sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right) \cos{\left(7 x \right)}\right) \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} + \frac{2 \left(7 x \cos{\left(7 x \right)} + \sin{\left(7 x \right)}\right) \sin^{2}{\left(7 x \right)}}{\sqrt{1 - x^{2}}} + \frac{49 \sin^{3}{\left(7 x \right)}}{\sqrt{1 - x^{2}}}\right)}{\cos^{2}{\left(6 x \right)}}
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Gráfico
Derivada de -((xsin7x)^3/((1-x^2)^((1/2)))+3*7(sin(7x)^2)*(1-x^2)^(1/2)*cos(7x))/(cos(6x)^2)
    © Sr Examen – Калькулятор