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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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- Derivada de:
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Derivada de e^x*sin(x)
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Derivada de x*e^(1/x)
- Derivada de x!
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Derivada de e^y
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Expresiones idénticas
- y=arcctg^ cuatro x*cos7x^4
- y es igual a arcctg en el grado 4x multiplicar por coseno de 7x en el grado 4
- y es igual a arcctg en el grado cuatro x multiplicar por coseno de 7x en el grado 4
- y=arcctg4x*cos7x4
- y=arcctg⁴x*cos7x⁴
- y=arcctg^4xcos7x^4
- y=arcctg4xcos7x4
Derivada de y=arcctg^4x*cos7x^4
Solución
Ha introducido
[src]
4 4 acot (x)*cos (7*x)
$$\cos^{4}{\left(7 x \right)} \operatorname{acot}^{4}{\left(x \right)}$$
acot(x)^4*cos(7*x)^4
Primera derivada
[src]
3 4
4 3 4*acot (x)*cos (7*x)
- 28*acot (x)*cos (7*x)*sin(7*x) - --------------------
2
1 + x
$$- 28 \sin{\left(7 x \right)} \cos^{3}{\left(7 x \right)} \operatorname{acot}^{4}{\left(x \right)} - \frac{4 \cos^{4}{\left(7 x \right)} \operatorname{acot}^{3}{\left(x \right)}}{x^{2} + 1}$$
Segunda derivada
[src]
/ 2 \
2 2 | 2 / 2 2 \ cos (7*x)*(3 + 2*x*acot(x)) 56*acot(x)*cos(7*x)*sin(7*x)|
4*acot (x)*cos (7*x)*|49*acot (x)*\- cos (7*x) + 3*sin (7*x)/ + --------------------------- + ----------------------------|
| 2 2 |
| / 2\ 1 + x |
\ \1 + x / /
$$4 \left(49 \left(3 \sin^{2}{\left(7 x \right)} - \cos^{2}{\left(7 x \right)}\right) \operatorname{acot}^{2}{\left(x \right)} + \frac{56 \sin{\left(7 x \right)} \cos{\left(7 x \right)} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{\left(2 x \operatorname{acot}{\left(x \right)} + 3\right) \cos^{2}{\left(7 x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \cos^{2}{\left(7 x \right)} \operatorname{acot}^{2}{\left(x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \ | 3 | 2 3 4*x *acot (x) 9*x*acot(x)| | |cos (7*x)*|- acot (x) + ------ + ------------- + -----------| | | | 2 2 2 | 2 / 2 2 \ 2 | | \ 1 + x 1 + x 1 + x / 3 / 2 2 \ 294*acot (x)*\- cos (7*x) + 3*sin (7*x)/*cos(7*x) 42*cos (7*x)*(3 + 2*x*acot(x))*acot(x)*sin(7*x)| -8*|------------------------------------------------------------- + 343*acot (x)*\- 5*cos (7*x) + 3*sin (7*x)/*sin(7*x) + ------------------------------------------------- + -----------------------------------------------|*acot(x)*cos(7*x) | 2 2 2 | | / 2\ 1 + x / 2\ | \ \1 + x / \1 + x / /
$$- 8 \left(343 \left(3 \sin^{2}{\left(7 x \right)} - 5 \cos^{2}{\left(7 x \right)}\right) \sin{\left(7 x \right)} \operatorname{acot}^{3}{\left(x \right)} + \frac{294 \left(3 \sin^{2}{\left(7 x \right)} - \cos^{2}{\left(7 x \right)}\right) \cos{\left(7 x \right)} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{42 \left(2 x \operatorname{acot}{\left(x \right)} + 3\right) \sin{\left(7 x \right)} \cos^{2}{\left(7 x \right)} \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\left(\frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{9 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \operatorname{acot}^{2}{\left(x \right)} + \frac{3}{x^{2} + 1}\right) \cos^{3}{\left(7 x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \cos{\left(7 x \right)} \operatorname{acot}{\left(x \right)}$$
Gráfico