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x^sin(5-2*x)
Derivada de la función/ x^sin/ 5-2*x/ x^sin(5-2*x)

Derivada de x^sin(5-2*x)

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

Gráfico:

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Solución

Ha introducido [src] 
 sin(5 - 2*x)
x
xsin⁡(5−2x)x^{\sin{\left(5 - 2 x \right)}} 
x^sin(5 - 2*x)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(sin⁡(5−2x))+1)sin⁡sin⁡(5−2x)(5−2x)\left(\log{\left(\sin{\left(5 - 2 x \right)} \right)} + 1\right) \sin^{\sin{\left(5 - 2 x \right)}}{\left(5 - 2 x \right)}

  2. Simplificamos:

    (−sin⁡(2x−5))−sin⁡(2x−5)(log⁡(−sin⁡(2x−5))+1)\left(- \sin{\left(2 x - 5 \right)}\right)^{- \sin{\left(2 x - 5 \right)}} \left(\log{\left(- \sin{\left(2 x - 5 \right)} \right)} + 1\right)

Respuesta:

(−sin⁡(2x−5))−sin⁡(2x−5)(log⁡(−sin⁡(2x−5))+1)\left(- \sin{\left(2 x - 5 \right)}\right)^{- \sin{\left(2 x - 5 \right)}} \left(\log{\left(- \sin{\left(2 x - 5 \right)} \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-100100
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Primera derivada [src] 
 sin(5 - 2*x) /sin(5 - 2*x)                         \
x            *|------------ - 2*cos(-5 + 2*x)*log(x)|
              \     x                               /
xsin⁡(5−2x)(−2log⁡(x)cos⁡(2x−5)+sin⁡(5−2x)x)x^{\sin{\left(5 - 2 x \right)}} \left(- 2 \log{\left(x \right)} \cos{\left(2 x - 5 \right)} + \frac{\sin{\left(5 - 2 x \right)}}{x}\right)
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Segunda derivada [src] 
                /                                        2                                                           \
 -sin(-5 + 2*x) |/sin(-5 + 2*x)                         \    sin(-5 + 2*x)   4*cos(-5 + 2*x)                         |
x              *||------------- + 2*cos(-5 + 2*x)*log(x)|  + ------------- - --------------- + 4*log(x)*sin(-5 + 2*x)|
                |\      x                               /           2               x                                |
                \                                                  x                                                 /
x−sin⁡(2x−5)((2log⁡(x)cos⁡(2x−5)+sin⁡(2x−5)x)2+4log⁡(x)sin⁡(2x−5)−4cos⁡(2x−5)x+sin⁡(2x−5)x2)x^{- \sin{\left(2 x - 5 \right)}} \left(\left(2 \log{\left(x \right)} \cos{\left(2 x - 5 \right)} + \frac{\sin{\left(2 x - 5 \right)}}{x}\right)^{2} + 4 \log{\left(x \right)} \sin{\left(2 x - 5 \right)} - \frac{4 \cos{\left(2 x - 5 \right)}}{x} + \frac{\sin{\left(2 x - 5 \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
                /                                          3                                                                                                                                                                                        \
 -sin(-5 + 2*x) |  /sin(-5 + 2*x)                         \      /sin(-5 + 2*x)                         \ /sin(-5 + 2*x)   4*cos(-5 + 2*x)                         \   2*sin(-5 + 2*x)   6*cos(-5 + 2*x)                            12*sin(-5 + 2*x)|
x              *|- |------------- + 2*cos(-5 + 2*x)*log(x)|  - 3*|------------- + 2*cos(-5 + 2*x)*log(x)|*|------------- - --------------- + 4*log(x)*sin(-5 + 2*x)| - --------------- + --------------- + 8*cos(-5 + 2*x)*log(x) + ----------------|
                |  \      x                               /      \      x                               / |       2               x                                |           3                 2                                         x        |
                \                                                                                         \      x                                                 /          x                 x                                                   /
x−sin⁡(2x−5)(−(2log⁡(x)cos⁡(2x−5)+sin⁡(2x−5)x)3−3(2log⁡(x)cos⁡(2x−5)+sin⁡(2x−5)x)(4log⁡(x)sin⁡(2x−5)−4cos⁡(2x−5)x+sin⁡(2x−5)x2)+8log⁡(x)cos⁡(2x−5)+12sin⁡(2x−5)x+6cos⁡(2x−5)x2−2sin⁡(2x−5)x3)x^{- \sin{\left(2 x - 5 \right)}} \left(- \left(2 \log{\left(x \right)} \cos{\left(2 x - 5 \right)} + \frac{\sin{\left(2 x - 5 \right)}}{x}\right)^{3} - 3 \left(2 \log{\left(x \right)} \cos{\left(2 x - 5 \right)} + \frac{\sin{\left(2 x - 5 \right)}}{x}\right) \left(4 \log{\left(x \right)} \sin{\left(2 x - 5 \right)} - \frac{4 \cos{\left(2 x - 5 \right)}}{x} + \frac{\sin{\left(2 x - 5 \right)}}{x^{2}}\right) + 8 \log{\left(x \right)} \cos{\left(2 x - 5 \right)} + \frac{12 \sin{\left(2 x - 5 \right)}}{x} + \frac{6 \cos{\left(2 x - 5 \right)}}{x^{2}} - \frac{2 \sin{\left(2 x - 5 \right)}}{x^{3}}\right)
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Gráfico
Derivada de x^sin(5-2*x)
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