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 1/(x+3)
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Derivada de 4*y
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Derivada de (2x-7)^8
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Derivada de (-1)/x-3*x
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Expresiones idénticas
- y=x*cos^3arctglnx
- y es igual a x multiplicar por coseno de al cubo arctglnx
- y=x*cos3arctglnx
- y=x*cos³arctglnx
- y=x*cos en el grado 3arctglnx
- y=xcos^3arctglnx
- y=xcos3arctglnx
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Expresiones con funciones
- Coseno cos
- cos(4*x+6)^(2)
- cos(log(x))+x^2*tan(x)
- cos(-6x+7)
- cos(3)+x^2
- cos(3*x)/3
Derivada de y=x*cos^3arctglnx
Solución
Ha introducido
[src]
3 x*cos (x)*atan(log(x))
$$x \cos^{3}{\left(x \right)} \operatorname{atan}{\left(\log{\left(x \right)} \right)}$$
(x*cos(x)^3)*atan(log(x))
Primera derivada
[src]
3
cos (x) / 3 2 \
----------- + \cos (x) - 3*x*cos (x)*sin(x)/*atan(log(x))
2
1 + log (x)
$$\left(- 3 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \cos^{3}{\left(x \right)}\right) \operatorname{atan}{\left(\log{\left(x \right)} \right)} + \frac{\cos^{3}{\left(x \right)}}{\log{\left(x \right)}^{2} + 1}$$
Segunda derivada
[src]
/ 2 / 2*log(x) \ \ | cos (x)*|1 + -----------| | | | 2 | | | / / 2 2 \ \ \ 1 + log (x)/ 2*(-cos(x) + 3*x*sin(x))*cos(x)| |3*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*atan(log(x)) - ------------------------- - -------------------------------|*cos(x) | / 2 \ / 2 \ | \ x*\1 + log (x)/ x*\1 + log (x)/ /
$$\left(3 \left(x \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \operatorname{atan}{\left(\log{\left(x \right)} \right)} - \frac{\left(1 + \frac{2 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 1}\right) \cos^{2}{\left(x \right)}}{x \left(\log{\left(x \right)}^{2} + 1\right)} - \frac{2 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \cos{\left(x \right)}}{x \left(\log{\left(x \right)}^{2} + 1\right)}\right) \cos{\left(x \right)}$$
Tercera derivada
[src]
/ 2 \
3 | 1 3*log(x) 4*log (x) |
2*cos (x)*|1 - ----------- + ----------- + --------------| 2 / 2*log(x) \
| 2 2 2| 3*cos (x)*|1 + -----------|*(-cos(x) + 3*x*sin(x))
| 1 + log (x) 1 + log (x) / 2 \ | / / 2 2 \ \ | 2 |
/ / 2 2 \ / 2 2 \ \ \ \1 + log (x)/ / 9*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*cos(x) \ 1 + log (x)/
- 3*\- 3*\- cos (x) + 2*sin (x)/*cos(x) + x*\- 7*cos (x) + 2*sin (x)/*sin(x)/*atan(log(x)) + ---------------------------------------------------------- + ------------------------------------------------------ + --------------------------------------------------
2 / 2 \ / 2 \ 2 / 2 \
x *\1 + log (x)/ x*\1 + log (x)/ x *\1 + log (x)/
$$- 3 \left(x \left(2 \sin^{2}{\left(x \right)} - 7 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} - 3 \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}\right) \operatorname{atan}{\left(\log{\left(x \right)} \right)} + \frac{9 \left(x \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \cos{\left(x \right)}}{x \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{3 \left(1 + \frac{2 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 1}\right) \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{2 \left(1 + \frac{3 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 1} - \frac{1}{\log{\left(x \right)}^{2} + 1} + \frac{4 \log{\left(x \right)}^{2}}{\left(\log{\left(x \right)}^{2} + 1\right)^{2}}\right) \cos^{3}{\left(x \right)}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)}$$
Gráfico