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 (-2)/x^3
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Expresiones idénticas
- (x*tgx)/arctgx
- (x multiplicar por tgx) dividir por arctgx
- (xtgx)/arctgx
- xtgx/arctgx
- (x*tgx) dividir por arctgx
Derivada de (x*tgx)/arctgx
Solución
Ha introducido
[src]
x*tan(x) -------- acot(x)
$$\frac{x \tan{\left(x \right)}}{\operatorname{acot}{\left(x \right)}}$$
(x*tan(x))/acot(x)
Primera derivada
[src]
/ 2 \
x*\1 + tan (x)/ + tan(x) x*tan(x)
------------------------ + -----------------
acot(x) / 2\ 2
\1 + x /*acot (x)
$$\frac{x \tan{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}}{\operatorname{acot}{\left(x \right)}}$$
Segunda derivada
[src]
/ / 1 \ \
| / 2 \ x*|x - -------|*tan(x)|
| 2 / 2 \ x*\1 + tan (x)/ + tan(x) \ acot(x)/ |
2*|1 + tan (x) + x*\1 + tan (x)/*tan(x) + ------------------------ - ----------------------|
| / 2\ 2 |
| \1 + x /*acot(x) / 2\ |
\ \1 + x / *acot(x) /
--------------------------------------------------------------------------------------------
acot(x)
$$\frac{2 \left(- \frac{x \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right) \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \tan^{2}{\left(x \right)} + 1 + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)}{\operatorname{acot}{\left(x \right)}}$$
Tercera derivada
[src]
/ / 2 \ \
| | 3 4*x 6*x | |
| / 1 \ / / 2 \ \ x*|-1 + ----------------- + ------ - ----------------|*tan(x)|
| / 2 / 2 \ \ 3*|x - -------|*\x*\1 + tan (x)/ + tan(x)/ | / 2\ 2 2 / 2\ | |
|/ 2 \ / / 2 \\ 3*\1 + tan (x) + x*\1 + tan (x)/*tan(x)/ \ acot(x)/ \ \1 + x /*acot (x) 1 + x \1 + x /*acot(x)/ |
2*|\1 + tan (x)/*\3*tan(x) + x*\1 + 3*tan (x)// + ---------------------------------------- - ------------------------------------------ + -------------------------------------------------------------|
| / 2\ 2 2 |
| \1 + x /*acot(x) / 2\ / 2\ |
\ \1 + x / *acot(x) \1 + x / *acot(x) /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
acot(x)
$$\frac{2 \left(\frac{x \left(\frac{4 x^{2}}{x^{2} + 1} - \frac{6 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - 1 + \frac{3}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}\right) \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} - \frac{3 \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right) \left(x \left(\tan^{2}{\left(x \right)} + 1\right) + \tan{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \left(x \left(3 \tan^{2}{\left(x \right)} + 1\right) + 3 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) + \frac{3 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)}{\operatorname{acot}{\left(x \right)}}$$
Gráfico