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^-(4/5)
-
Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- y=(tgx/ tres)/arctg4x
- y es igual a (tgx dividir por 3) dividir por arctg4x
- y es igual a (tgx dividir por tres) dividir por arctg4x
- y=tgx/3/arctg4x
- y=(tgx dividir por 3) dividir por arctg4x
Derivada de y=(tgx/3)/arctg4x
Solución
Ha introducido
[src]
/tan(x)\ |------| \ 3 / --------- atan(4*x)
$$\frac{\frac{1}{3} \tan{\left(x \right)}}{\operatorname{atan}{\left(4 x \right)}}$$
(tan(x)/3)/atan(4*x)
Primera derivada
[src]
2
1 tan (x)
- + -------
3 3 4*tan(x)
----------- - ------------------------
atan(4*x) / 2\ 2
3*\1 + 16*x /*atan (4*x)
$$\frac{\frac{\tan^{2}{\left(x \right)}}{3} + \frac{1}{3}}{\operatorname{atan}{\left(4 x \right)}} - \frac{4 \tan{\left(x \right)}}{3 \left(16 x^{2} + 1\right) \operatorname{atan}^{2}{\left(4 x \right)}}$$
Segunda derivada
[src]
/ / 1 \ \
| / 2 \ 16*|--------- + 4*x|*tan(x)|
|/ 2 \ 4*\1 + tan (x)/ \atan(4*x) / |
2*|\1 + tan (x)/*tan(x) - --------------------- + ---------------------------|
| / 2\ 2 |
| \1 + 16*x /*atan(4*x) / 2\ |
\ \1 + 16*x / *atan(4*x) /
------------------------------------------------------------------------------
3*atan(4*x)
$$\frac{2 \left(\frac{16 \left(4 x + \frac{1}{\operatorname{atan}{\left(4 x \right)}}\right) \tan{\left(x \right)}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right)}{3 \operatorname{atan}{\left(4 x \right)}}$$
Tercera derivada
[src]
/ / 2 \ \
| | 3 64*x 24*x | |
| / 2 \ / 1 \ 64*|-1 + ---------------------- + --------- + ---------------------|*tan(x)|
|/ 2 \ / 2 \ / 2 \ 16*\1 + tan (x)/*|--------- + 4*x| | / 2\ 2 2 / 2\ | |
|\1 + tan (x)/*\1 + 3*tan (x)/ 4*\1 + tan (x)/*tan(x) \atan(4*x) / \ \1 + 16*x /*atan (4*x) 1 + 16*x \1 + 16*x /*atan(4*x)/ |
2*|----------------------------- - ---------------------- + ---------------------------------- - ---------------------------------------------------------------------------|
| 3 / 2\ 2 2 |
| \1 + 16*x /*atan(4*x) / 2\ / 2\ |
\ \1 + 16*x / *atan(4*x) 3*\1 + 16*x / *atan(4*x) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
atan(4*x)
$$\frac{2 \left(\frac{16 \left(4 x + \frac{1}{\operatorname{atan}{\left(4 x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 1\right)}{3} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - \frac{64 \left(\frac{64 x^{2}}{16 x^{2} + 1} + \frac{24 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - 1 + \frac{3}{\left(16 x^{2} + 1\right) \operatorname{atan}^{2}{\left(4 x \right)}}\right) \tan{\left(x \right)}}{3 \left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}}\right)}{\operatorname{atan}{\left(4 x \right)}}$$
Gráfico