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=(arctg2x)x(ctg4x)
- y es igual a (arctg2x)x(ctg4x)
- y=arctg2xxctg4x
Derivada de y=(arctg2x)x(ctg4x)
Solución
Ha introducido
[src]
atan(2*x)*x*cot(4*x)
$$x \operatorname{atan}{\left(2 x \right)} \cot{\left(4 x \right)}$$
(atan(2*x)*x)*cot(4*x)
Primera derivada
[src]
/ 2*x \ / 2 \ |-------- + atan(2*x)|*cot(4*x) + x*\-4 - 4*cot (4*x)/*atan(2*x) | 2 | \1 + 4*x /
$$x \left(- 4 \cot^{2}{\left(4 x \right)} - 4\right) \operatorname{atan}{\left(2 x \right)} + \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \cot{\left(4 x \right)}$$
Segunda derivada
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/ / 2 \ \ | | 4*x | | | |-1 + --------|*cot(4*x) | | | 2| | | / 2 \ / 2*x \ \ 1 + 4*x / / 2 \ | 4*|- 2*\1 + cot (4*x)/*|-------- + atan(2*x)| - ------------------------ + 8*x*\1 + cot (4*x)/*atan(2*x)*cot(4*x)| | | 2 | 2 | \ \1 + 4*x / 1 + 4*x /
$$4 \left(8 x \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)} - 2 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \left(\cot^{2}{\left(4 x \right)} + 1\right) - \frac{\left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \cot{\left(4 x \right)}}{4 x^{2} + 1}\right)$$
Tercera derivada
[src]
/ / 2 \ / 2 \ \ | / 2 \ | 4*x | | 4*x | | |3*\1 + cot (4*x)/*|-1 + --------| 4*x*|-1 + --------|*cot(4*x)| | | 2| | 2| | | \ 1 + 4*x / / 2 \ / 2*x \ / 2 \ / 2 \ \ 1 + 4*x / | 16*|--------------------------------- + 6*\1 + cot (4*x)/*|-------- + atan(2*x)|*cot(4*x) - 8*x*\1 + cot (4*x)/*\1 + 3*cot (4*x)/*atan(2*x) + ----------------------------| | 2 | 2 | 2 | | 1 + 4*x \1 + 4*x / / 2\ | \ \1 + 4*x / /
$$16 \left(- 8 x \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(3 \cot^{2}{\left(4 x \right)} + 1\right) \operatorname{atan}{\left(2 x \right)} + \frac{4 x \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \cot{\left(4 x \right)}}{\left(4 x^{2} + 1\right)^{2}} + 6 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)} + \frac{3 \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \left(\cot^{2}{\left(4 x \right)} + 1\right)}{4 x^{2} + 1}\right)$$
Gráfico