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 y=-6/x
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Expresiones idénticas
- y=tg^ cuatro *arcctg^ dos
- y es igual a tg en el grado 4 multiplicar por arcctg al cuadrado
- y es igual a tg en el grado cuatro multiplicar por arcctg en el grado dos
- y=tg4*arcctg2
- y=tg⁴*arcctg²
- y=tg en el grado 4*arcctg en el grado 2
- y=tg^4arcctg^2
- y=tg4arcctg2
Derivada de y=tg^4*arcctg^2
Solución
Ha introducido
[src]
4 2 tan (x)*acot (x)
$$\tan^{4}{\left(x \right)} \operatorname{acot}^{2}{\left(x \right)}$$
tan(x)^4*acot(x)^2
Primera derivada
[src]
4
2 3 / 2 \ 2*tan (x)*acot(x)
acot (x)*tan (x)*\4 + 4*tan (x)/ - -----------------
2
1 + x
$$\left(4 \tan^{2}{\left(x \right)} + 4\right) \tan^{3}{\left(x \right)} \operatorname{acot}^{2}{\left(x \right)} - \frac{2 \tan^{4}{\left(x \right)} \operatorname{acot}{\left(x \right)}}{x^{2} + 1}$$
Segunda derivada
[src]
/ 2 / 2 \ \
2 |tan (x)*(1 + 2*x*acot(x)) 2 / 2 \ / 2 \ 8*\1 + tan (x)/*acot(x)*tan(x)|
2*tan (x)*|------------------------- + 2*acot (x)*\1 + tan (x)/*\3 + 5*tan (x)/ - ------------------------------|
| 2 2 |
| / 2\ 1 + x |
\ \1 + x / /
$$2 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(5 \tan^{2}{\left(x \right)} + 3\right) \operatorname{acot}^{2}{\left(x \right)} - \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{\left(2 x \operatorname{acot}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \tan^{2}{\left(x \right)}$$
Tercera derivada
[src]
/ / 2 \ \ | 3 | 3*x 4*x *acot(x)| | | tan (x)*|-acot(x) + ------ + ------------| | | | 2 2 | / 2 \ 2 / 2 \ / 2 \ / 2 \ | | \ 1 + x 1 + x / 2 / 2 \ | 4 / 2 \ 2 / 2 \| 6*tan (x)*\1 + tan (x)/*(1 + 2*x*acot(x)) 6*\1 + tan (x)/*\3 + 5*tan (x)/*acot(x)*tan(x)| 4*|- ------------------------------------------ + 2*acot (x)*\1 + tan (x)/*\2*tan (x) + 3*\1 + tan (x)/ + 10*tan (x)*\1 + tan (x)// + ----------------------------------------- - ----------------------------------------------|*tan(x) | 2 2 2 | | / 2\ / 2\ 1 + x | \ \1 + x / \1 + x / /
$$4 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 10 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 2 \tan^{4}{\left(x \right)}\right) \operatorname{acot}^{2}{\left(x \right)} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(5 \tan^{2}{\left(x \right)} + 3\right) \tan{\left(x \right)} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{6 \left(2 x \operatorname{acot}{\left(x \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{\left(\frac{4 x^{2} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right) \tan^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \tan{\left(x \right)}$$
Gráfico