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y=(x²+1)^sinx
Derivada de la función/ y=(x²+1)/ y=(x²+1)^sinx

Derivada de y=(x²+1)^sinx

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

Ha introducido [src] 
        sin(x)
/ 2    \      
\x  + 1/
(x2+1)sin⁡(x)\left(x^{2} + 1\right)^{\sin{\left(x \right)}} 
(x^2 + 1)^sin(x)
Solución detallada

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

    Perola derivada

    (log⁡(sin⁡(x))+1)sin⁡sin⁡(x)(x)\left(\log{\left(\sin{\left(x \right)} \right)} + 1\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}

Respuesta:

(log⁡(sin⁡(x))+1)sin⁡sin⁡(x)(x)\left(\log{\left(\sin{\left(x \right)} \right)} + 1\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}

Gráfica
02468-8-6-4-2-1010-200200
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        sin(x)                                  
/ 2    \       /          / 2    \   2*x*sin(x)\
\x  + 1/      *|cos(x)*log\x  + 1/ + ----------|
               |                        2      |
               \                       x  + 1  /
(x2+1)sin⁡(x)(2xsin⁡(x)x2+1+log⁡(x2+1)cos⁡(x))\left(x^{2} + 1\right)^{\sin{\left(x \right)}} \left(\frac{2 x \sin{\left(x \right)}}{x^{2} + 1} + \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)}\right)
Simplificar
Segunda derivada [src] 
        sin(x) /                                 2                                      2                    \
/     2\       |/          /     2\   2*x*sin(x)\       /     2\          2*sin(x)   4*x *sin(x)   4*x*cos(x)|
\1 + x /      *||cos(x)*log\1 + x / + ----------|  - log\1 + x /*sin(x) + -------- - ----------- + ----------|
               ||                            2  |                               2             2           2  |
               |\                       1 + x   /                          1 + x      /     2\       1 + x   |
               \                                                                      \1 + x /               /
(x2+1)sin⁡(x)(−4x2sin⁡(x)(x2+1)2+4xcos⁡(x)x2+1+(2xsin⁡(x)x2+1+log⁡(x2+1)cos⁡(x))2−log⁡(x2+1)sin⁡(x)+2sin⁡(x)x2+1)\left(x^{2} + 1\right)^{\sin{\left(x \right)}} \left(- \frac{4 x^{2} \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{4 x \cos{\left(x \right)}}{x^{2} + 1} + \left(\frac{2 x \sin{\left(x \right)}}{x^{2} + 1} + \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)}\right)^{2} - \log{\left(x^{2} + 1 \right)} \sin{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x^{2} + 1}\right)
Simplificar
Tercera derivada [src] 
        sin(x) /                                 3                                                            /                                                2       \                                2                           3       \
/     2\       |/          /     2\   2*x*sin(x)\              /     2\     /          /     2\   2*x*sin(x)\ |   /     2\          2*sin(x)   4*x*cos(x)   4*x *sin(x)|   6*cos(x)   12*x*sin(x)   12*x *cos(x)   6*x*sin(x)   16*x *sin(x)|
\1 + x /      *||cos(x)*log\1 + x / + ----------|  - cos(x)*log\1 + x / - 3*|cos(x)*log\1 + x / + ----------|*|log\1 + x /*sin(x) - -------- - ---------- + -----------| + -------- - ----------- - ------------ - ---------- + ------------|
               ||                            2  |                           |                            2  | |                           2           2              2 |         2             2             2            2              3  |
               |\                       1 + x   /                           \                       1 + x   / |                      1 + x       1 + x       /     2\  |    1 + x      /     2\      /     2\        1 + x       /     2\   |
               \                                                                                              \                                              \1 + x /  /               \1 + x /      \1 + x /                    \1 + x /   /
(x2+1)sin⁡(x)(16x3sin⁡(x)(x2+1)3−12x2cos⁡(x)(x2+1)2−6xsin⁡(x)x2+1−12xsin⁡(x)(x2+1)2+(2xsin⁡(x)x2+1+log⁡(x2+1)cos⁡(x))3−3(2xsin⁡(x)x2+1+log⁡(x2+1)cos⁡(x))(4x2sin⁡(x)(x2+1)2−4xcos⁡(x)x2+1+log⁡(x2+1)sin⁡(x)−2sin⁡(x)x2+1)−log⁡(x2+1)cos⁡(x)+6cos⁡(x)x2+1)\left(x^{2} + 1\right)^{\sin{\left(x \right)}} \left(\frac{16 x^{3} \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x^{2} \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6 x \sin{\left(x \right)}}{x^{2} + 1} - \frac{12 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \sin{\left(x \right)}}{x^{2} + 1} + \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)}\right)^{3} - 3 \left(\frac{2 x \sin{\left(x \right)}}{x^{2} + 1} + \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)}\right) \left(\frac{4 x^{2} \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{4 x \cos{\left(x \right)}}{x^{2} + 1} + \log{\left(x^{2} + 1 \right)} \sin{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{x^{2} + 1}\right) - \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)} + \frac{6 \cos{\left(x \right)}}{x^{2} + 1}\right)
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Gráfico
Derivada de y=(x²+1)^sinx
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