Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de 1/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- y=(lnx)^sin(5x)
- y es igual a (lnx) en el grado seno de (5x)
- y=(lnx)sin(5x)
- y=lnxsin5x
- y=lnx^sin5x
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Expresiones con funciones
- Seno sin
- sin(x)cos(x)
- sin(t)*cos(t)
- sin(3*x^2)/((3*x^2))
- sin(3*x-pi/12)
- sin(5*x+2)
Derivada de y=(lnx)^sin(5x)
Solución
Ha introducido
[src]
sin(5*x) log (x)
$$\log{\left(x \right)}^{\sin{\left(5 x \right)}}$$
log(x)^sin(5*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
sin(5*x) / sin(5*x)\
log (x)*|5*cos(5*x)*log(log(x)) + --------|
\ x*log(x)/
$$\left(5 \log{\left(\log{\left(x \right)} \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\sin{\left(5 x \right)}}$$
Segunda derivada
[src]
/ 2 \
sin(5*x) |/ sin(5*x)\ sin(5*x) sin(5*x) 10*cos(5*x)|
log (x)*||5*cos(5*x)*log(log(x)) + --------| - 25*log(log(x))*sin(5*x) - --------- - ---------- + -----------|
|\ x*log(x)/ 2 2 2 x*log(x) |
\ x *log(x) x *log (x) /
$$\left(\left(5 \log{\left(\log{\left(x \right)} \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x \log{\left(x \right)}}\right)^{2} - 25 \log{\left(\log{\left(x \right)} \right)} \sin{\left(5 x \right)} + \frac{10 \cos{\left(5 x \right)}}{x \log{\left(x \right)}} - \frac{\sin{\left(5 x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\sin{\left(5 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{\sin{\left(5 x \right)}}$$
Tercera derivada
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/ 3 \
sin(5*x) |/ sin(5*x)\ / sin(5*x)\ / sin(5*x) sin(5*x) 10*cos(5*x)\ 75*sin(5*x) 15*cos(5*x) 15*cos(5*x) 2*sin(5*x) 2*sin(5*x) 3*sin(5*x)|
log (x)*||5*cos(5*x)*log(log(x)) + --------| - 125*cos(5*x)*log(log(x)) - 3*|5*cos(5*x)*log(log(x)) + --------|*|25*log(log(x))*sin(5*x) + --------- + ---------- - -----------| - ----------- - ----------- - ----------- + ---------- + ---------- + ----------|
|\ x*log(x)/ \ x*log(x)/ | 2 2 2 x*log(x) | x*log(x) 2 2 2 3 3 3 3 2 |
\ \ x *log(x) x *log (x) / x *log(x) x *log (x) x *log(x) x *log (x) x *log (x)/
$$\left(\left(5 \log{\left(\log{\left(x \right)} \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x \log{\left(x \right)}}\right)^{3} - 3 \left(5 \log{\left(\log{\left(x \right)} \right)} \cos{\left(5 x \right)} + \frac{\sin{\left(5 x \right)}}{x \log{\left(x \right)}}\right) \left(25 \log{\left(\log{\left(x \right)} \right)} \sin{\left(5 x \right)} - \frac{10 \cos{\left(5 x \right)}}{x \log{\left(x \right)}} + \frac{\sin{\left(5 x \right)}}{x^{2} \log{\left(x \right)}} + \frac{\sin{\left(5 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) - 125 \log{\left(\log{\left(x \right)} \right)} \cos{\left(5 x \right)} - \frac{75 \sin{\left(5 x \right)}}{x \log{\left(x \right)}} - \frac{15 \cos{\left(5 x \right)}}{x^{2} \log{\left(x \right)}} - \frac{15 \cos{\left(5 x \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \sin{\left(5 x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \sin{\left(5 x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \sin{\left(5 x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{\sin{\left(5 x \right)}}$$
Gráfico