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^4/3-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
- x*exp(arctgsinx)
- x multiplicar por exponente de (arctg seno de x)
- xexp(arctgsinx)
- xexparctgsinx
Derivada de x*exp(arctgsinx)
Solución
Ha introducido
[src]
atan(sin(x)) x*e
$$x e^{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}$$
x*exp(atan(sin(x)))
Primera derivada
[src]
atan(sin(x))
x*cos(x)*e atan(sin(x))
---------------------- + e
2
1 + sin (x)
$$\frac{x e^{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}} \cos{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} + e^{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}$$
Segunda derivada
[src]
/ / 2 2 \\
| | cos (x) 2*cos (x)*sin(x) || atan(sin(x))
|2*cos(x) - x*|- ----------- + ---------------- + sin(x)||*e
| | 2 2 ||
\ \ 1 + sin (x) 1 + sin (x) //
------------------------------------------------------------------------
2
1 + sin (x)
$$\frac{\left(- x \left(\sin{\left(x \right)} + \frac{2 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}\right) + 2 \cos{\left(x \right)}\right) e^{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}}{\sin^{2}{\left(x \right)} + 1}$$
Tercera derivada
[src]
/ 2 / 2 2 2 2 2 2 \ 2 \
| 3*cos (x) | cos (x) 6*sin (x) 2*cos (x) 3*sin(x) 8*cos (x)*sin (x) 6*cos (x)*sin(x)| 6*cos (x)*sin(x)| atan(sin(x))
-|3*sin(x) - ----------- + x*|1 - -------------- - ----------- + ----------- + ----------- - ----------------- + ----------------|*cos(x) + ----------------|*e
| 2 | 2 2 2 2 2 2 | 2 |
| 1 + sin (x) | / 2 \ 1 + sin (x) 1 + sin (x) 1 + sin (x) / 2 \ / 2 \ | 1 + sin (x) |
\ \ \1 + sin (x)/ \1 + sin (x)/ \1 + sin (x)/ / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
1 + sin (x)
$$- \frac{\left(x \left(1 - \frac{6 \sin^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} + \frac{3 \sin{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} + \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} - \frac{8 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\sin^{2}{\left(x \right)} + 1\right)^{2}} + \frac{6 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\sin^{2}{\left(x \right)} + 1\right)^{2}} - \frac{\cos^{2}{\left(x \right)}}{\left(\sin^{2}{\left(x \right)} + 1\right)^{2}}\right) \cos{\left(x \right)} + 3 \sin{\left(x \right)} + \frac{6 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} - \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}\right) e^{\operatorname{atan}{\left(\sin{\left(x \right)} \right)}}}{\sin^{2}{\left(x \right)} + 1}$$
Gráfico