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 e^x*sin(x)
- Derivada de x!
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Derivada de e^x*x^3
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Derivada de e^x/x^2
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Expresiones idénticas
- y=(x*cos^ tres)arctglnx
- y es igual a (x multiplicar por coseno de al cubo )arctglnx
- y es igual a (x multiplicar por coseno de en el grado tres)arctglnx
- y=(x*cos3)arctglnx
- y=x*cos3arctglnx
- y=(x*cos³)arctglnx
- y=(x*cos en el grado 3)arctglnx
- y=(xcos^3)arctglnx
- y=(xcos3)arctglnx
- y=xcos3arctglnx
- y=xcos^3arctglnx
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Expresiones con funciones
- Coseno cos
- cos(3)^(2)*x
- cos(5-3*x)
- cos/sin
- cos(7*x)
- cos(x+1)/2
Derivada de y=(x*cos^3)arctglnx
Solución
Ha introducido
[src]
3 x*cos (x)*atan(x)*log(x)
$$x \cos^{3}{\left(x \right)} \operatorname{atan}{\left(x \right)} \log{\left(x \right)}$$
((x*cos(x)^3)*atan(x))*log(x)
Primera derivada
[src]
/ 3 \
3 |/ 3 2 \ x*cos (x)|
cos (x)*atan(x) + |\cos (x) - 3*x*cos (x)*sin(x)/*atan(x) + ---------|*log(x)
| 2 |
\ 1 + x /
$$\left(\frac{x \cos^{3}{\left(x \right)}}{x^{2} + 1} + \left(- 3 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \cos^{3}{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}\right) \log{\left(x \right)} + \cos^{3}{\left(x \right)} \operatorname{atan}{\left(x \right)}$$
Segunda derivada
[src]
/ / x*cos(x)\ \ | 2*|-(-cos(x) + 3*x*sin(x))*atan(x) + --------|*cos(x)| | / 2 2 \ 2 | 2 | | | | / / 2 2 \ \ 2*x *cos (x) 2*(-cos(x) + 3*x*sin(x))*cos(x)| cos (x)*atan(x) \ 1 + x / | |- |- 3*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*atan(x) + ------------ + -------------------------------|*log(x) - --------------- + -----------------------------------------------------|*cos(x) | | 2 2 | x x | | | / 2\ 1 + x | | \ \ \1 + x / / /
$$\left(- \left(\frac{2 x^{2} \cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - 3 \left(x \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} + \frac{2 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \cos{\left(x \right)}}{x^{2} + 1}\right) \log{\left(x \right)} + \frac{2 \left(\frac{x \cos{\left(x \right)}}{x^{2} + 1} - \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}\right) \cos{\left(x \right)}}{x} - \frac{\cos^{2}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x}\right) \cos{\left(x \right)}$$
Tercera derivada
[src]
/ 2 2 \ / / 2 \ \ | / / 2 2 \ \ 2*x *cos (x) 2*(-cos(x) + 3*x*sin(x))*cos(x)| | 3 | 4*x | | 3*|- 3*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*atan(x) + ------------ + -------------------------------|*cos(x) 2 / x*cos(x)\ | 2*x*cos (x)*|-1 + ------| | | 2 2 | 3*cos (x)*|-(-cos(x) + 3*x*sin(x))*atan(x) + --------| | / / 2 2 \ \ | 2| 2 | | / 2\ 1 + x | | 2 | 3 | / / 2 2 \ / 2 2 \ \ 9*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*cos(x) \ 1 + x / 6*x*cos (x)*(-cos(x) + 3*x*sin(x))| \ \1 + x / / \ 1 + x / 2*cos (x)*atan(x) |- 3*\- 3*\- cos (x) + 2*sin (x)/*cos(x) + x*\- 7*cos (x) + 2*sin (x)/*sin(x)/*atan(x) + ------------------------------------------------------ + ------------------------- + ----------------------------------|*log(x) - --------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------ + ----------------- | 2 2 2 | x 2 2 | 1 + x / 2\ / 2\ | x x \ \1 + x / \1 + x / /
$$\left(\frac{6 x \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \cos^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - 3 \left(x \left(2 \sin^{2}{\left(x \right)} - 7 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} - 3 \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} + \frac{9 \left(x \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \cos{\left(x \right)}}{x^{2} + 1}\right) \log{\left(x \right)} - \frac{3 \left(\frac{2 x^{2} \cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - 3 \left(x \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} + \frac{2 \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \cos{\left(x \right)}}{x^{2} + 1}\right) \cos{\left(x \right)}}{x} - \frac{3 \left(\frac{x \cos{\left(x \right)}}{x^{2} + 1} - \left(3 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{x^{2}} + \frac{2 \cos^{3}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2}}$$
Gráfico