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^(3*x)
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Derivada de -2x
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Derivada de x^3*sin(x)
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Derivada de (sqrt(x)-1)/sqrt(x^2-x-1)
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Expresiones idénticas
- arctg((tgx-ctgx)/sqrt(dos))
- arctg((tgx menos ctgx) dividir por raíz cuadrada de (2))
- arctg((tgx menos ctgx) dividir por raíz cuadrada de (dos))
- arctg((tgx-ctgx)/√(2))
- arctgtgx-ctgx/sqrt2
- arctg((tgx-ctgx) dividir por sqrt(2))
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Expresiones semejantes
- arctg((tgx+ctgx)/sqrt(2))
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Expresiones con funciones
- arctg
- arctg(sinx)
- arctg(3x)
- arctg2x
- arctg1/x
- arctg(2x)
- tgx
- tgx/(sinx-cosx)
- tgx-2cosx
- tgx/x
- tgx-9x
- tgx-ctgx
- Raíz cuadrada sqrt
- sqrt
- sqrt3x
- sqrt(3*x)
- sqrt(x)^2
- sqrt(x^2-3)
Derivada de arctg((tgx-ctgx)/sqrt(2))
Solución
Ha introducido
[src]
/tan(x) - cot(x)\
atan|---------------|
| ___ |
\ \/ 2 /
$$\operatorname{atan}{\left(\frac{\tan{\left(x \right)} - \cot{\left(x \right)}}{\sqrt{2}} \right)}$$
atan((tan(x) - cot(x))/sqrt(2))
Primera derivada
[src]
___ / 2 2 \
\/ 2 *\2 + cot (x) + tan (x)/
-----------------------------
/ 2\
| (tan(x) - cot(x)) |
2*|1 + ------------------|
\ 2 /
$$\frac{\sqrt{2} \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)}{2 \left(\frac{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2}}{2} + 1\right)}$$
Segunda derivada
[src]
/ 2 \
| / 2 2 \ |
___ |/ 2 \ / 2 \ \2 + cot (x) + tan (x)/ *(-cot(x) + tan(x))|
2*\/ 2 *|\1 + tan (x)/*tan(x) - \1 + cot (x)/*cot(x) - -------------------------------------------|
| 2 |
\ 2 + (-cot(x) + tan(x)) /
---------------------------------------------------------------------------------------------------
2
2 + (-cot(x) + tan(x))
$$\frac{2 \sqrt{2} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - \frac{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)^{2}}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2}\right)}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2}$$
Tercera derivada
[src]
/ 3 3 \
| 2 2 / 2 2 \ 2 / 2 2 \ // 2 \ / 2 \ \ / 2 2 \|
___ |/ 2 \ / 2 \ \2 + cot (x) + tan (x)/ 2 / 2 \ 2 / 2 \ 4*(-cot(x) + tan(x)) *\2 + cot (x) + tan (x)/ 6*(-cot(x) + tan(x))*\\1 + tan (x)/*tan(x) - \1 + cot (x)/*cot(x)/*\2 + cot (x) + tan (x)/|
2*\/ 2 *|\1 + cot (x)/ + \1 + tan (x)/ - ------------------------ + 2*cot (x)*\1 + cot (x)/ + 2*tan (x)*\1 + tan (x)/ + ---------------------------------------------- - ------------------------------------------------------------------------------------------|
| 2 2 2 |
| 2 + (-cot(x) + tan(x)) / 2\ 2 + (-cot(x) + tan(x)) |
\ \2 + (-cot(x) + tan(x)) / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
2 + (-cot(x) + tan(x))
$$\frac{2 \sqrt{2} \left(- \frac{6 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \left(\tan{\left(x \right)} - \cot{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2} + \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \left(\cot^{2}{\left(x \right)} + 1\right)^{2} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} - \frac{\left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)^{3}}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2} + \frac{4 \left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)^{3}}{\left(\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2\right)^{2}}\right)}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2}$$
Gráfico