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^-(4/5)
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- y=(arctg2x)^sinx
- y es igual a (arctg2x) en el grado seno de x
- y=(arctg2x)sinx
- y=arctg2xsinx
- y=arctg2x^sinx
Derivada de y=(arctg2x)^sinx
Solución
Ha introducido
[src]
sin(x) atan (2*x)
$$\operatorname{atan}^{\sin{\left(x \right)}}{\left(2 x \right)}$$
atan(2*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) / 2*sin(x) \
atan (2*x)*|cos(x)*log(atan(2*x)) + --------------------|
| / 2\ |
\ \1 + 4*x /*atan(2*x)/
$$\left(\log{\left(\operatorname{atan}{\left(2 x \right)} \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}\right) \operatorname{atan}^{\sin{\left(x \right)}}{\left(2 x \right)}$$
Segunda derivada
[src]
/ 2 \
sin(x) |/ 2*sin(x) \ 4*sin(x) 4*cos(x) 16*x*sin(x) |
atan (2*x)*||cos(x)*log(atan(2*x)) + --------------------| - log(atan(2*x))*sin(x) - ---------------------- + -------------------- - ---------------------|
|| / 2\ | 2 / 2\ 2 |
|\ \1 + 4*x /*atan(2*x)/ / 2\ 2 \1 + 4*x /*atan(2*x) / 2\ |
\ \1 + 4*x / *atan (2*x) \1 + 4*x / *atan(2*x)/
$$\left(- \frac{16 x \sin{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \left(\log{\left(\operatorname{atan}{\left(2 x \right)} \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}\right)^{2} - \log{\left(\operatorname{atan}{\left(2 x \right)} \right)} \sin{\left(x \right)} + \frac{4 \cos{\left(x \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{4 \sin{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(2 x \right)}}\right) \operatorname{atan}^{\sin{\left(x \right)}}{\left(2 x \right)}$$
Tercera derivada
[src]
/ 3 2 \
sin(x) |/ 2*sin(x) \ / 2*sin(x) \ / 4*cos(x) 4*sin(x) 16*x*sin(x) \ 16*sin(x) 12*cos(x) 6*sin(x) 16*sin(x) 48*x*cos(x) 96*x*sin(x) 256*x *sin(x) |
atan (2*x)*||cos(x)*log(atan(2*x)) + --------------------| - cos(x)*log(atan(2*x)) - 3*|cos(x)*log(atan(2*x)) + --------------------|*|log(atan(2*x))*sin(x) - -------------------- + ---------------------- + ---------------------| - --------------------- - ---------------------- - -------------------- + ---------------------- - --------------------- + ---------------------- + ---------------------|
|| / 2\ | | / 2\ | | / 2\ 2 2 | 2 2 / 2\ 3 2 3 3 |
|\ \1 + 4*x /*atan(2*x)/ \ \1 + 4*x /*atan(2*x)/ | \1 + 4*x /*atan(2*x) / 2\ 2 / 2\ | / 2\ / 2\ 2 \1 + 4*x /*atan(2*x) / 2\ 3 / 2\ / 2\ 2 / 2\ |
\ \ \1 + 4*x / *atan (2*x) \1 + 4*x / *atan(2*x)/ \1 + 4*x / *atan(2*x) \1 + 4*x / *atan (2*x) \1 + 4*x / *atan (2*x) \1 + 4*x / *atan(2*x) \1 + 4*x / *atan (2*x) \1 + 4*x / *atan(2*x)/
$$\left(\frac{256 x^{2} \sin{\left(x \right)}}{\left(4 x^{2} + 1\right)^{3} \operatorname{atan}{\left(2 x \right)}} - \frac{48 x \cos{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \frac{96 x \sin{\left(x \right)}}{\left(4 x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(2 x \right)}} + \left(\log{\left(\operatorname{atan}{\left(2 x \right)} \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}\right)^{3} - 3 \left(\log{\left(\operatorname{atan}{\left(2 x \right)} \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}}\right) \left(\frac{16 x \sin{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \log{\left(\operatorname{atan}{\left(2 x \right)} \right)} \sin{\left(x \right)} - \frac{4 \cos{\left(x \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \frac{4 \sin{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(2 x \right)}}\right) - \log{\left(\operatorname{atan}{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{6 \sin{\left(x \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{16 \sin{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} - \frac{12 \cos{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(2 x \right)}} + \frac{16 \sin{\left(x \right)}}{\left(4 x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(2 x \right)}}\right) \operatorname{atan}^{\sin{\left(x \right)}}{\left(2 x \right)}$$
Gráfico