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^-8
-
Derivada de x^2/lnx
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Derivada de √x+2
-
Derivada de (t^(2)+1)÷(t^(1÷2)-1)
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Expresiones idénticas
- y=arctanh(logtan(x))
- y es igual a arc tangente de gente hiperbólica de ( logaritmo de tangente de (x))
- y=arctanhlogtanx
Derivada de y=arctanh(logtan(x))
Solución
Ha introducido
[src]
atanh(log(x)*tan(x))
$$\operatorname{atanh}{\left(\log{\left(x \right)} \tan{\left(x \right)} \right)}$$
atanh(log(x)*tan(x))
Primera derivada
[src]
tan(x) / 2 \
------ + \1 + tan (x)/*log(x)
x
-----------------------------
2 2
1 - log (x)*tan (x)
$$\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}}{- \log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} + 1}$$
Segunda derivada
[src]
2
/tan(x) / 2 \ \
/ 2 \ 2*|------ + \1 + tan (x)/*log(x)| *log(x)*tan(x)
tan(x) 2*\1 + tan (x)/ / 2 \ \ x /
------ - --------------- - 2*\1 + tan (x)/*log(x)*tan(x) + ------------------------------------------------
2 x 2 2
x -1 + log (x)*tan (x)
-----------------------------------------------------------------------------------------------------------
2 2
-1 + log (x)*tan (x)
$$\frac{\frac{2 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} \tan{\left(x \right)}}{\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{\tan{\left(x \right)}}{x^{2}}}{\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1}$$
Tercera derivada
[src]
/ 2 2 2 / 2 \ \ / / 2 \ \
/tan(x) / 2 \ \ |tan (x) / 2 \ 2 tan (x)*log(x) 2 2 / 2 \ 4*\1 + tan (x)/*log(x)*tan(x)| 3 /tan(x) / 2 \ \ | tan(x) 2*\1 + tan (x)/ / 2 \ |
2*|------ + \1 + tan (x)/*log(x)|*|------- + \1 + tan (x)/ *log (x) - -------------- + 2*log (x)*tan (x)*\1 + tan (x)/ + -----------------------------| /tan(x) / 2 \ \ 2 2 4*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|*log(x)*tan(x)
2 / 2 \ / 2 \ \ x / | 2 2 x | 8*|------ + \1 + tan (x)/*log(x)| *log (x)*tan (x) \ x / | 2 x |
2*tan(x) / 2 \ 3*\1 + tan (x)/ 6*\1 + tan (x)/*tan(x) 2 / 2 \ \ x x / \ x / \ x /
- -------- - 2*\1 + tan (x)/ *log(x) + --------------- - ---------------------- - 4*tan (x)*\1 + tan (x)/*log(x) + ------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------- + ------------------------------------------------------------------------------------------------------------
3 2 x 2 2 2 2 2
x x -1 + log (x)*tan (x) / 2 2 \ -1 + log (x)*tan (x)
\-1 + log (x)*tan (x)/
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
-1 + log (x)*tan (x)
$$\frac{- \frac{8 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} \log{\left(x \right)}^{2} \tan^{2}{\left(x \right)}}{\left(\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1\right)^{2}} + \frac{4 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \tan{\left(x \right)}}{\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1} + \frac{2 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)}}{x} - \frac{\log{\left(x \right)} \tan^{2}{\left(x \right)}}{x^{2}} + \frac{\tan^{2}{\left(x \right)}}{x^{2}}\right)}{\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1} - 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} - 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} - \frac{2 \tan{\left(x \right)}}{x^{3}}}{\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1}$$
Gráfico