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Derivada de la función/ cos^(7)(4x^(3)-((5)/(x))+4x)

Derivada de cos^(7)(4x^(3)-((5)/(x))+4x)

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

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Solución

Ha introducido [src] 
   7/   3   5      \
cos |4*x  - - + 4*x|
    \       x      /
cos⁡7(4x+(4x3−5x))\cos^{7}{\left(4 x + \left(4 x^{3} - \frac{5}{x}\right) \right)} 
cos(4*x^3 - 5/x + 4*x)^7
Primera derivada [src] 
      6/   3   5      \ /    5        2\    /   3   5      \
-7*cos |4*x  - - + 4*x|*|4 + -- + 12*x |*sin|4*x  - - + 4*x|
       \       x      / |     2        |    \       x      /
                        \    x         /
−7(12x2+4+5x2)sin⁡(4x+(4x3−5x))cos⁡6(4x+(4x3−5x))- 7 \left(12 x^{2} + 4 + \frac{5}{x^{2}}\right) \sin{\left(4 x + \left(4 x^{3} - \frac{5}{x}\right) \right)} \cos^{6}{\left(4 x + \left(4 x^{3} - \frac{5}{x}\right) \right)}
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Segunda derivada [src] 
                         /                  2                                            2                                                                                     \
     5/  5            3\ |  /    5        2\     2/  5            3\     /    5        2\     2/  5            3\     /  5        \    /  5            3\    /  5            3\|
7*cos |- - + 4*x + 4*x |*|- |4 + -- + 12*x | *cos |- - + 4*x + 4*x | + 6*|4 + -- + 12*x | *sin |- - + 4*x + 4*x | - 2*|- -- + 12*x|*cos|- - + 4*x + 4*x |*sin|- - + 4*x + 4*x ||
      \  x             / |  |     2        |      \  x             /     |     2        |      \  x             /     |   3       |    \  x             /    \  x             /|
                         \  \    x         /                             \    x         /                             \  x        /                                            /
7(−2(12x−5x3)sin⁡(4x3+4x−5x)cos⁡(4x3+4x−5x)+6(12x2+4+5x2)2sin⁡2(4x3+4x−5x)−(12x2+4+5x2)2cos⁡2(4x3+4x−5x))cos⁡5(4x3+4x−5x)7 \left(- 2 \left(12 x - \frac{5}{x^{3}}\right) \sin{\left(4 x^{3} + 4 x - \frac{5}{x} \right)} \cos{\left(4 x^{3} + 4 x - \frac{5}{x} \right)} + 6 \left(12 x^{2} + 4 + \frac{5}{x^{2}}\right)^{2} \sin^{2}{\left(4 x^{3} + 4 x - \frac{5}{x} \right)} - \left(12 x^{2} + 4 + \frac{5}{x^{2}}\right)^{2} \cos^{2}{\left(4 x^{3} + 4 x - \frac{5}{x} \right)}\right) \cos^{5}{\left(4 x^{3} + 4 x - \frac{5}{x} \right)}
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Tercera derivada [src] 
                         /                     3                                                                                                                                                                 3                                                                                                                              \
     4/  5            3\ |     /    5        2\     3/  5            3\        2/  5            3\ /    5 \    /  5            3\        3/  5            3\ /  5        \ /    5        2\      /    5        2\     2/  5            3\    /  5            3\         2/  5            3\ /  5        \ /    5        2\    /  5            3\|
7*cos |- - + 4*x + 4*x |*|- 30*|4 + -- + 12*x | *sin |- - + 4*x + 4*x | - 6*cos |- - + 4*x + 4*x |*|4 + --|*sin|- - + 4*x + 4*x | - 6*cos |- - + 4*x + 4*x |*|- -- + 12*x|*|4 + -- + 12*x | + 19*|4 + -- + 12*x | *cos |- - + 4*x + 4*x |*sin|- - + 4*x + 4*x | + 36*sin |- - + 4*x + 4*x |*|- -- + 12*x|*|4 + -- + 12*x |*cos|- - + 4*x + 4*x ||
      \  x             / |     |     2        |      \  x             /         \  x             / |     4|    \  x             /         \  x             / |   3       | |     2        |      |     2        |      \  x             /    \  x             /          \  x             / |   3       | |     2        |    \  x             /|
                         \     \    x         /                                                    \    x /                                                  \  x        / \    x         /      \    x         /                                                                           \  x        / \    x         /                      /
7(−6(4+5x4)sin⁡(4x3+4x−5x)cos⁡2(4x3+4x−5x)+36(12x−5x3)(12x2+4+5x2)sin⁡2(4x3+4x−5x)cos⁡(4x3+4x−5x)−6(12x−5x3)(12x2+4+5x2)cos⁡3(4x3+4x−5x)−30(12x2+4+5x2)3sin⁡3(4x3+4x−5x)+19(12x2+4+5x2)3sin⁡(4x3+4x−5x)cos⁡2(4x3+4x−5x))cos⁡4(4x3+4x−5x)7 \left(- 6 \left(4 + \frac{5}{x^{4}}\right) \sin{\left(4 x^{3} + 4 x - \frac{5}{x} \right)} \cos^{2}{\left(4 x^{3} + 4 x - \frac{5}{x} \right)} + 36 \left(12 x - \frac{5}{x^{3}}\right) \left(12 x^{2} + 4 + \frac{5}{x^{2}}\right) \sin^{2}{\left(4 x^{3} + 4 x - \frac{5}{x} \right)} \cos{\left(4 x^{3} + 4 x - \frac{5}{x} \right)} - 6 \left(12 x - \frac{5}{x^{3}}\right) \left(12 x^{2} + 4 + \frac{5}{x^{2}}\right) \cos^{3}{\left(4 x^{3} + 4 x - \frac{5}{x} \right)} - 30 \left(12 x^{2} + 4 + \frac{5}{x^{2}}\right)^{3} \sin^{3}{\left(4 x^{3} + 4 x - \frac{5}{x} \right)} + 19 \left(12 x^{2} + 4 + \frac{5}{x^{2}}\right)^{3} \sin{\left(4 x^{3} + 4 x - \frac{5}{x} \right)} \cos^{2}{\left(4 x^{3} + 4 x - \frac{5}{x} \right)}\right) \cos^{4}{\left(4 x^{3} + 4 x - \frac{5}{x} \right)}
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