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 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=arctgx\ dos *cosx^ tres
- y es igual a arctgx\2 multiplicar por coseno de x al cubo
- y es igual a arctgx\ dos multiplicar por coseno de x en el grado tres
- y=arctgx\2*cosx3
- y=arctgx\2*cosx³
- y=arctgx\2*cosx en el grado 3
- y=arctgx\2cosx^3
- y=arctgx\2cosx3
Derivada de y=arctgx\2*cosx^3
Solución
Ha introducido
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acot(x) 3 -------*cos (x) 2
$$\frac{\operatorname{acot}{\left(x \right)}}{2} \cos^{3}{\left(x \right)}$$
(acot(x)/2)*cos(x)^3
Primera derivada
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3 2
cos (x) 3*cos (x)*acot(x)*sin(x)
- ---------- - ------------------------
/ 2\ 2
2*\1 + x /
$$- \frac{3 \sin{\left(x \right)} \cos^{2}{\left(x \right)} \operatorname{acot}{\left(x \right)}}{2} - \frac{\cos^{3}{\left(x \right)}}{2 \left(x^{2} + 1\right)}$$
Segunda derivada
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/ / 2 2 \ 2 \ |3*\- cos (x) + 2*sin (x)/*acot(x) x*cos (x) 3*cos(x)*sin(x)| |--------------------------------- + --------- + ---------------|*cos(x) | 2 2 2 | | / 2\ 1 + x | \ \1 + x / /
$$\left(\frac{x \cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{acot}{\left(x \right)}}{2} + \frac{3 \sin{\left(x \right)} \cos{\left(x \right)}}{x^{2} + 1}\right) \cos{\left(x \right)}$$
3-я производная
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/ / 2 \ \ | 3 | 4*x | | |cos (x)*|-1 + ------| | | | 2| / 2 2 \ / 2 2 \ 2 | | \ 1 + x / 3*\- 7*cos (x) + 2*sin (x)/*acot(x)*sin(x) 9*\- cos (x) + 2*sin (x)/*cos(x) 9*x*cos (x)*sin(x)| -|--------------------- + ------------------------------------------ + -------------------------------- + ------------------| | 2 2 / 2\ 2 | | / 2\ 2*\1 + x / / 2\ | \ \1 + x / \1 + x / /
$$- (\frac{9 x \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(2 \sin^{2}{\left(x \right)} - 7 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{acot}{\left(x \right)}}{2} + \frac{9 \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}}{2 \left(x^{2} + 1\right)} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \cos^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}})$$
Tercera derivada
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/ / 2 \ \ | 3 | 4*x | | |cos (x)*|-1 + ------| | | | 2| / 2 2 \ / 2 2 \ 2 | | \ 1 + x / 3*\- 7*cos (x) + 2*sin (x)/*acot(x)*sin(x) 9*\- cos (x) + 2*sin (x)/*cos(x) 9*x*cos (x)*sin(x)| -|--------------------- + ------------------------------------------ + -------------------------------- + ------------------| | 2 2 / 2\ 2 | | / 2\ 2*\1 + x / / 2\ | \ \1 + x / \1 + x / /
$$- (\frac{9 x \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(2 \sin^{2}{\left(x \right)} - 7 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{acot}{\left(x \right)}}{2} + \frac{9 \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}}{2 \left(x^{2} + 1\right)} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \cos^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}})$$
Gráfico