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Derivada de la función/ x^2+2/ y=3^sin^7(x^2+2/√x)

Derivada de y=3^sin^7(x^2+2/√x)

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

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Solución

Ha introducido [src] 
    7/ 2     2  \
 sin |x  + -----|
     |       ___|
     \     \/ x /
3
3sin⁡7(x2+2x)3^{\sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}} 
3^(sin(x^2 + 2/sqrt(x))^7)
Primera derivada [src] 
      7/ 2     2  \                                                       
   sin |x  + -----|                                                       
       |       ___|                                                       
       \     \/ x /    6/ 2     2  \ /   1        \    / 2     2  \       
7*3                *sin |x  + -----|*|- ---- + 2*x|*cos|x  + -----|*log(3)
                        |       ___| |   3/2      |    |       ___|       
                        \     \/ x / \  x         /    \     \/ x /
7⋅3sin⁡7(x2+2x)(2x−1x32)log⁡(3)sin⁡6(x2+2x)cos⁡(x2+2x)7 \cdot 3^{\sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}} \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right) \log{\left(3 \right)} \sin^{6}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}
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Segunda derivada [src] 
      7/ 2     2  \                  /                                                                          /     3  \    / 2     2  \    / 2     2  \                                                             \       
   sin |x  + -----|                  |                                                                          |4 + ----|*cos|x  + -----|*sin|x  + -----|                                                             |       
       |       ___|                  |                2                                    2                    |     5/2|    |       ___|    |       ___|                   2                                         |       
       \     \/ x /    5/ 2     2  \ |  /   1        \     2/ 2     2  \     /   1        \     2/ 2     2  \   \    x   /    \     \/ x /    \     \/ x /     /   1        \     2/ 2     2  \    7/ 2     2  \       |       
7*3                *sin |x  + -----|*|- |- ---- + 2*x| *sin |x  + -----| + 6*|- ---- + 2*x| *cos |x  + -----| + ------------------------------------------ + 7*|- ---- + 2*x| *cos |x  + -----|*sin |x  + -----|*log(3)|*log(3)
                        |       ___| |  |   3/2      |      |       ___|     |   3/2      |      |       ___|                       2                          |   3/2      |      |       ___|     |       ___|       |       
                        \     \/ x / \  \  x         /      \     \/ x /     \  x         /      \     \/ x /                                                  \  x         /      \     \/ x /     \     \/ x /       /
7⋅3sin⁡7(x2+2x)((4+3x52)sin⁡(x2+2x)cos⁡(x2+2x)2+7(2x−1x32)2log⁡(3)sin⁡7(x2+2x)cos⁡2(x2+2x)−(2x−1x32)2sin⁡2(x2+2x)+6(2x−1x32)2cos⁡2(x2+2x))log⁡(3)sin⁡5(x2+2x)7 \cdot 3^{\sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}} \left(\frac{\left(4 + \frac{3}{x^{\frac{5}{2}}}\right) \sin{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}}{2} + 7 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{2} \log{\left(3 \right)} \sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} - \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{2} \sin^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} + 6 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{2} \cos^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}\right) \log{\left(3 \right)} \sin^{5}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}
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Tercera derivada [src] 
      7/ 2     2  \                  /                                                                                                  2/ 2     2  \    / 2     2  \        3/ 2     2  \ /     3  \ /   1        \                                                                                                                                                                                                                                                                    2/ 2     2  \    8/ 2     2  \ /     3  \ /   1        \       \       
   sin |x  + -----|                  |                                                                                            15*sin |x  + -----|*cos|x  + -----|   3*sin |x  + -----|*|4 + ----|*|- ---- + 2*x|                                                                                                                                                                                                                                                              21*cos |x  + -----|*sin |x  + -----|*|4 + ----|*|- ---- + 2*x|*log(3)|       
       |       ___|                  |                 3                                     3                                           |       ___|    |       ___|         |       ___| |     5/2| |   3/2      |                    3                                                                                                                           3                                                                3                                                   |       ___|     |       ___| |     5/2| |   3/2      |       |       
       \     \/ x /    4/ 2     2  \ |   /   1        \     3/ 2     2  \      /   1        \     2/ 2     2  \    / 2     2  \          \     \/ x /    \     \/ x /         \     \/ x / \    x   / \  x         /      /   1        \     9/ 2     2  \    / 2     2  \               2/ 2     2  \ /     3  \ /   1        \    / 2     2  \      /   1        \     3/ 2     2  \    2       14/ 2     2  \       /   1        \     3/ 2     2  \    7/ 2     2  \                 \     \/ x /     \     \/ x / \    x   / \  x         /       |       
7*3                *sin |x  + -----|*|30*|- ---- + 2*x| *cos |x  + -----| - 19*|- ---- + 2*x| *sin |x  + -----|*cos|x  + -----| - ----------------------------------- - -------------------------------------------- - 21*|- ---- + 2*x| *sin |x  + -----|*cos|x  + -----|*log(3) + 9*cos |x  + -----|*|4 + ----|*|- ---- + 2*x|*sin|x  + -----| + 49*|- ---- + 2*x| *cos |x  + -----|*log (3)*sin  |x  + -----| + 126*|- ---- + 2*x| *cos |x  + -----|*sin |x  + -----|*log(3) + ---------------------------------------------------------------------|*log(3)
                        |       ___| |   |   3/2      |      |       ___|      |   3/2      |      |       ___|    |       ___|                     7/2                                      2                            |   3/2      |      |       ___|    |       ___|                |       ___| |     5/2| |   3/2      |    |       ___|      |   3/2      |      |       ___|              |       ___|       |   3/2      |      |       ___|     |       ___|                                            2                                  |       
                        \     \/ x / \   \  x         /      \     \/ x /      \  x         /      \     \/ x /    \     \/ x /                  4*x                                                                      \  x         /      \     \/ x /    \     \/ x /                \     \/ x / \    x   / \  x         /    \     \/ x /      \  x         /      \     \/ x /              \     \/ x /       \  x         /      \     \/ x /     \     \/ x /                                                                               /
7⋅3sin⁡7(x2+2x)(21(4+3x52)(2x−1x32)log⁡(3)sin⁡8(x2+2x)cos⁡2(x2+2x)2−3(4+3x52)(2x−1x32)sin⁡3(x2+2x)2+9(4+3x52)(2x−1x32)sin⁡(x2+2x)cos⁡2(x2+2x)+49(2x−1x32)3log⁡(3)2sin⁡14(x2+2x)cos⁡3(x2+2x)−21(2x−1x32)3log⁡(3)sin⁡9(x2+2x)cos⁡(x2+2x)+126(2x−1x32)3log⁡(3)sin⁡7(x2+2x)cos⁡3(x2+2x)−19(2x−1x32)3sin⁡2(x2+2x)cos⁡(x2+2x)+30(2x−1x32)3cos⁡3(x2+2x)−15sin⁡2(x2+2x)cos⁡(x2+2x)4x72)log⁡(3)sin⁡4(x2+2x)7 \cdot 3^{\sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}} \left(\frac{21 \left(4 + \frac{3}{x^{\frac{5}{2}}}\right) \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right) \log{\left(3 \right)} \sin^{8}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}}{2} - \frac{3 \left(4 + \frac{3}{x^{\frac{5}{2}}}\right) \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right) \sin^{3}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}}{2} + 9 \left(4 + \frac{3}{x^{\frac{5}{2}}}\right) \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right) \sin{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} + 49 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{3} \log{\left(3 \right)}^{2} \sin^{14}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos^{3}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} - 21 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{3} \log{\left(3 \right)} \sin^{9}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} + 126 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{3} \log{\left(3 \right)} \sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos^{3}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} - 19 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{3} \sin^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} + 30 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{3} \cos^{3}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} - \frac{15 \sin^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}}{4 x^{\frac{7}{2}}}\right) \log{\left(3 \right)} \sin^{4}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}
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