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 x^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de y=-6/x
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Expresiones idénticas
- y=(arctgx)^sinx
- y es igual a (arctgx) en el grado seno de x
- y=(arctgx)sinx
- y=arctgxsinx
- y=arctgx^sinx
Derivada de y=(arctgx)^sinx
Solución
Ha introducido
[src]
sin(x) acot (x)
$$\operatorname{acot}^{\sin{\left(x \right)}}{\left(x \right)}$$
acot(x)^sin(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(x) / sin(x) \
acot (x)*|cos(x)*log(acot(x)) - ----------------|
| / 2\ |
\ \1 + x /*acot(x)/
$$\left(\log{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right) \operatorname{acot}^{\sin{\left(x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ 2 \
sin(x) |/ sin(x) \ sin(x) 2*cos(x) 2*x*sin(x) |
acot (x)*||cos(x)*log(acot(x)) - ----------------| - log(acot(x))*sin(x) - ------------------ - ---------------- + -----------------|
|| / 2\ | 2 / 2\ 2 |
|\ \1 + x /*acot(x)/ / 2\ 2 \1 + x /*acot(x) / 2\ |
\ \1 + x / *acot (x) \1 + x / *acot(x)/
$$\left(\frac{2 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \left(\log{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)^{2} - \log{\left(\operatorname{acot}{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - \frac{\sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}}\right) \operatorname{acot}^{\sin{\left(x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ 3 2 \
sin(x) |/ sin(x) \ / sin(x) \ / sin(x) 2*cos(x) 2*x*sin(x) \ 3*cos(x) 2*sin(x) 2*sin(x) 3*sin(x) 8*x *sin(x) 6*x*sin(x) 6*x*cos(x) |
acot (x)*||cos(x)*log(acot(x)) - ----------------| - cos(x)*log(acot(x)) - 3*|cos(x)*log(acot(x)) - ----------------|*|log(acot(x))*sin(x) + ------------------ + ---------------- - -----------------| - ------------------ - ------------------ + ----------------- + ---------------- - ----------------- + ------------------ + -----------------|
|| / 2\ | | / 2\ | | 2 / 2\ 2 | 2 3 2 / 2\ 3 3 2 |
|\ \1 + x /*acot(x)/ \ \1 + x /*acot(x)/ | / 2\ 2 \1 + x /*acot(x) / 2\ | / 2\ 2 / 2\ 3 / 2\ \1 + x /*acot(x) / 2\ / 2\ 2 / 2\ |
\ \ \1 + x / *acot (x) \1 + x / *acot(x)/ \1 + x / *acot (x) \1 + x / *acot (x) \1 + x / *acot(x) \1 + x / *acot(x) \1 + x / *acot (x) \1 + x / *acot(x)/
$$\left(- \frac{8 x^{2} \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{acot}{\left(x \right)}} + \frac{6 x \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \frac{6 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{acot}^{2}{\left(x \right)}} + \left(\log{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)^{3} - 3 \left(\log{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(x \right)} - \frac{\sin{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right) \left(- \frac{2 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \log{\left(\operatorname{acot}{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}}\right) - \log{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{2 \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{2}{\left(x \right)}} - \frac{2 \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{acot}^{3}{\left(x \right)}}\right) \operatorname{acot}^{\sin{\left(x \right)}}{\left(x \right)}$$
Gráfico