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:
-
Derivada de (-4)/x^2
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Derivada de 2/x²
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Derivada de -2*y
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Derivada de (3+2x)/(x-5)
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Expresiones idénticas
- (xtg6x)/(arctg4x)
- (xtg6x) dividir por (arctg4x)
- xtg6x/arctg4x
Derivada de (xtg6x)/(arctg4x)
Solución
Ha introducido
[src]
x*tan(6*x) ---------- atan(4*x)
$$\frac{x \tan{\left(6 x \right)}}{\operatorname{atan}{\left(4 x \right)}}$$
(x*tan(6*x))/atan(4*x)
Primera derivada
[src]
/ 2 \
x*\6 + 6*tan (6*x)/ + tan(6*x) 4*x*tan(6*x)
------------------------------ - ----------------------
atan(4*x) / 2\ 2
\1 + 16*x /*atan (4*x)
$$- \frac{4 x \tan{\left(6 x \right)}}{\left(16 x^{2} + 1\right) \operatorname{atan}^{2}{\left(4 x \right)}} + \frac{x \left(6 \tan^{2}{\left(6 x \right)} + 6\right) + \tan{\left(6 x \right)}}{\operatorname{atan}{\left(4 x \right)}}$$
Segunda derivada
[src]
/ / 1 \ \
| / / 2 \ \ 8*x*|--------- + 4*x|*tan(6*x)|
| 2 2*\6*x*\1 + tan (6*x)/ + tan(6*x)/ / 2 \ \atan(4*x) / |
4*|3 + 3*tan (6*x) - ---------------------------------- + 18*x*\1 + tan (6*x)/*tan(6*x) + ------------------------------|
| / 2\ 2 |
| \1 + 16*x /*atan(4*x) / 2\ |
\ \1 + 16*x / *atan(4*x) /
-------------------------------------------------------------------------------------------------------------------------
atan(4*x)
$$\frac{4 \left(\frac{8 x \left(4 x + \frac{1}{\operatorname{atan}{\left(4 x \right)}}\right) \tan{\left(6 x \right)}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + 18 x \left(\tan^{2}{\left(6 x \right)} + 1\right) \tan{\left(6 x \right)} + 3 \tan^{2}{\left(6 x \right)} + 3 - \frac{2 \left(6 x \left(\tan^{2}{\left(6 x \right)} + 1\right) + \tan{\left(6 x \right)}\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right)}{\operatorname{atan}{\left(4 x \right)}}$$
Tercera derivada
[src]
/ / 2 \ \
| | 3 64*x 24*x | |
| / 1 \ / / 2 \ \ 16*x*|-1 + ---------------------- + --------- + ---------------------|*tan(6*x)|
| / 2 / 2 \ \ 12*|--------- + 4*x|*\6*x*\1 + tan (6*x)/ + tan(6*x)/ | / 2\ 2 2 / 2\ | |
| / 2 \ / / 2 \ \ 18*\1 + tan (6*x) + 6*x*\1 + tan (6*x)/*tan(6*x)/ \atan(4*x) / \ \1 + 16*x /*atan (4*x) 1 + 16*x \1 + 16*x /*atan(4*x)/ |
8*|27*\1 + tan (6*x)/*\2*x*\1 + 3*tan (6*x)/ + tan(6*x)/ - ------------------------------------------------- + ----------------------------------------------------- - -------------------------------------------------------------------------------|
| / 2\ 2 2 |
| \1 + 16*x /*atan(4*x) / 2\ / 2\ |
\ \1 + 16*x / *atan(4*x) \1 + 16*x / *atan(4*x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
atan(4*x)
$$\frac{8 \left(- \frac{16 x \left(\frac{64 x^{2}}{16 x^{2} + 1} + \frac{24 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - 1 + \frac{3}{\left(16 x^{2} + 1\right) \operatorname{atan}^{2}{\left(4 x \right)}}\right) \tan{\left(6 x \right)}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + \frac{12 \left(4 x + \frac{1}{\operatorname{atan}{\left(4 x \right)}}\right) \left(6 x \left(\tan^{2}{\left(6 x \right)} + 1\right) + \tan{\left(6 x \right)}\right)}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + 27 \left(2 x \left(3 \tan^{2}{\left(6 x \right)} + 1\right) + \tan{\left(6 x \right)}\right) \left(\tan^{2}{\left(6 x \right)} + 1\right) - \frac{18 \left(6 x \left(\tan^{2}{\left(6 x \right)} + 1\right) \tan{\left(6 x \right)} + \tan^{2}{\left(6 x \right)} + 1\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right)}{\operatorname{atan}{\left(4 x \right)}}$$
Gráfico