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
-
¿Cómo usar?
- Derivada de:
-
Derivada de x+2
-
Derivada de -(x^2+49)/x
-
Derivada de y=2x+5
-
Derivada de sqrt(x)*sin(x)
-
Expresiones idénticas
- arctg^ dos (sinx)
- arctg al cuadrado ( seno de x)
- arctg en el grado dos ( seno de x)
- arctg2(sinx)
- arctg2sinx
- arctg²(sinx)
- arctg en el grado 2(sinx)
- arctg^2sinx
-
Expresiones con funciones
- arctg
- arctg(3x)^2
- arctg
- arctg(lnx)
- arctg(x^2)
- arctg(x/2)
- sinx
- sinx^3
- sinx/x^4
- sinx
- sinxlnx
- sinx/x
Derivada de arctg^2(sinx)
Solución
Ha introducido
[src]
2 atan (sin(x))
$$\operatorname{atan}^{2}{\left(\sin{\left(x \right)} \right)}$$
atan(sin(x))^2
Primera derivada
[src]
2*atan(sin(x))*cos(x)
---------------------
2
1 + sin (x)
$$\frac{2 \cos{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} + 1}$$
Segunda derivada
[src]
/ 2 2 \
| cos (x) 2*cos (x)*atan(sin(x))*sin(x)|
2*|----------- - atan(sin(x))*sin(x) - -----------------------------|
| 2 2 |
\1 + sin (x) 1 + sin (x) /
---------------------------------------------------------------------
2
1 + sin (x)
$$\frac{2 \left(- \sin{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)} - \frac{2 \sin{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} + 1} + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}\right)}{\sin^{2}{\left(x \right)} + 1}$$
Tercera derivada
[src]
/ 2 2 2 2 2 \
| 3*sin(x) 6*cos (x)*sin(x) 2*cos (x)*atan(sin(x)) 6*sin (x)*atan(sin(x)) 8*cos (x)*sin (x)*atan(sin(x))|
2*|-atan(sin(x)) - ----------- - ---------------- - ---------------------- + ---------------------- + ------------------------------|*cos(x)
| 2 2 2 2 2 |
| 1 + sin (x) / 2 \ 1 + sin (x) 1 + sin (x) / 2 \ |
\ \1 + sin (x)/ \1 + sin (x)/ /
--------------------------------------------------------------------------------------------------------------------------------------------
2
1 + sin (x)
$$\frac{2 \left(- \operatorname{atan}{\left(\sin{\left(x \right)} \right)} + \frac{6 \sin^{2}{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} + 1} - \frac{3 \sin{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} - \frac{2 \cos^{2}{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)} + 1} + \frac{8 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{atan}{\left(\sin{\left(x \right)} \right)}}{\left(\sin^{2}{\left(x \right)} + 1\right)^{2}} - \frac{6 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\sin^{2}{\left(x \right)} + 1\right)^{2}}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}$$
Gráfico