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:
-
Derivada de x^4/3-x
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Derivada de x^-4/5
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Derivada de x=1
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Derivada de x^2*2^x
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Expresiones idénticas
- y=arctg^ dos (cosx)
- y es igual a arctg al cuadrado ( coseno de x)
- y es igual a arctg en el grado dos ( coseno de x)
- y=arctg2(cosx)
- y=arctg2cosx
- y=arctg²(cosx)
- y=arctg en el grado 2(cosx)
- y=arctg^2cosx
Derivada de y=arctg^2(cosx)
Solución
Ha introducido
[src]
2 atan (cos(x))
$$\operatorname{atan}^{2}{\left(\cos{\left(x \right)} \right)}$$
atan(cos(x))^2
Primera derivada
[src]
-2*atan(cos(x))*sin(x)
----------------------
2
1 + cos (x)
$$- \frac{2 \sin{\left(x \right)} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} + 1}$$
Segunda derivada
[src]
/ 2 2 \
| sin (x) 2*sin (x)*atan(cos(x))*cos(x)|
2*|----------- - atan(cos(x))*cos(x) - -----------------------------|
| 2 2 |
\1 + cos (x) 1 + cos (x) /
---------------------------------------------------------------------
2
1 + cos (x)
$$\frac{2 \left(- \cos{\left(x \right)} \operatorname{atan}{\left(\cos{\left(x \right)} \right)} - \frac{2 \sin^{2}{\left(x \right)} \cos{\left(x \right)} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} + 1} + \frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)} + 1}\right)}{\cos^{2}{\left(x \right)} + 1}$$
Tercera derivada
[src]
/ 2 2 2 2 2 \
| 3*cos(x) 6*cos (x)*atan(cos(x)) 2*sin (x)*atan(cos(x)) 6*sin (x)*cos(x) 8*cos (x)*sin (x)*atan(cos(x)) |
2*|----------- - ---------------------- + ---------------------- + ---------------- - ------------------------------ + atan(cos(x))|*sin(x)
| 2 2 2 2 2 |
|1 + cos (x) 1 + cos (x) 1 + cos (x) / 2 \ / 2 \ |
\ \1 + cos (x)/ \1 + cos (x)/ /
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2
1 + cos (x)
$$\frac{2 \left(\operatorname{atan}{\left(\cos{\left(x \right)} \right)} + \frac{2 \sin^{2}{\left(x \right)} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} + 1} - \frac{6 \cos^{2}{\left(x \right)} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} + 1} + \frac{3 \cos{\left(x \right)}}{\cos^{2}{\left(x \right)} + 1} - \frac{8 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{atan}{\left(\cos{\left(x \right)} \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{2}} + \frac{6 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} + 1\right)^{2}}\right) \sin{\left(x \right)}}{\cos^{2}{\left(x \right)} + 1}$$
Gráfico