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y=(x-5)^cos3x

Derivada de y=(x-5)^cos3x

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Solución

Ha introducido [src]
       cos(3*x)
(x - 5)        
$$\left(x - 5\right)^{\cos{\left(3 x \right)}}$$
(x - 5)^cos(3*x)
Solución detallada
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    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
       cos(3*x) /cos(3*x)                        \
(x - 5)        *|-------- - 3*log(x - 5)*sin(3*x)|
                \ x - 5                          /
$$\left(x - 5\right)^{\cos{\left(3 x \right)}} \left(- 3 \log{\left(x - 5 \right)} \sin{\left(3 x \right)} + \frac{\cos{\left(3 x \right)}}{x - 5}\right)$$
Segunda derivada [src]
                 /                                     2                                                  \
        cos(3*x) |/  cos(3*x)                         \     cos(3*x)                            6*sin(3*x)|
(-5 + x)        *||- -------- + 3*log(-5 + x)*sin(3*x)|  - --------- - 9*cos(3*x)*log(-5 + x) - ----------|
                 |\   -5 + x                          /            2                              -5 + x  |
                 \                                         (-5 + x)                                       /
$$\left(x - 5\right)^{\cos{\left(3 x \right)}} \left(\left(3 \log{\left(x - 5 \right)} \sin{\left(3 x \right)} - \frac{\cos{\left(3 x \right)}}{x - 5}\right)^{2} - 9 \log{\left(x - 5 \right)} \cos{\left(3 x \right)} - \frac{6 \sin{\left(3 x \right)}}{x - 5} - \frac{\cos{\left(3 x \right)}}{\left(x - 5\right)^{2}}\right)$$
Tercera derivada [src]
                 /                                       3                                                                                                                                                              \
        cos(3*x) |  /  cos(3*x)                         \    27*cos(3*x)   2*cos(3*x)     /  cos(3*x)                         \ / cos(3*x)   6*sin(3*x)                         \   9*sin(3*x)                          |
(-5 + x)        *|- |- -------- + 3*log(-5 + x)*sin(3*x)|  - ----------- + ---------- + 3*|- -------- + 3*log(-5 + x)*sin(3*x)|*|--------- + ---------- + 9*cos(3*x)*log(-5 + x)| + ---------- + 27*log(-5 + x)*sin(3*x)|
                 |  \   -5 + x                          /       -5 + x             3      \   -5 + x                          / |        2     -5 + x                           |           2                           |
                 \                                                         (-5 + x)                                             \(-5 + x)                                       /   (-5 + x)                            /
$$\left(x - 5\right)^{\cos{\left(3 x \right)}} \left(- \left(3 \log{\left(x - 5 \right)} \sin{\left(3 x \right)} - \frac{\cos{\left(3 x \right)}}{x - 5}\right)^{3} + 3 \left(3 \log{\left(x - 5 \right)} \sin{\left(3 x \right)} - \frac{\cos{\left(3 x \right)}}{x - 5}\right) \left(9 \log{\left(x - 5 \right)} \cos{\left(3 x \right)} + \frac{6 \sin{\left(3 x \right)}}{x - 5} + \frac{\cos{\left(3 x \right)}}{\left(x - 5\right)^{2}}\right) + 27 \log{\left(x - 5 \right)} \sin{\left(3 x \right)} - \frac{27 \cos{\left(3 x \right)}}{x - 5} + \frac{9 \sin{\left(3 x \right)}}{\left(x - 5\right)^{2}} + \frac{2 \cos{\left(3 x \right)}}{\left(x - 5\right)^{3}}\right)$$
Gráfico
Derivada de y=(x-5)^cos3x