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 2^√x
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Derivada de 3^(1/x)
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Derivada de 2*x+8/x
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Derivada de -1/y
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Expresiones idénticas
- y=ctg^34x*arctg dos x^2
- y es igual a ctg al cubo 4x multiplicar por arctg2x al cuadrado
- y es igual a ctg al cubo 4x multiplicar por arctg dos x al cuadrado
- y=ctg34x*arctg2x2
- y=ctg³4x*arctg2x²
- y=ctg en el grado 34x*arctg2x en el grado 2
- y=ctg^34xarctg2x^2
- y=ctg34xarctg2x2
Derivada de y=ctg^34x*arctg2x^2
Solución
Ha introducido
[src]
3 2 cot (4*x)*atan (2*x)
$$\cot^{3}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}$$
cot(4*x)^3*atan(2*x)^2
Primera derivada
[src]
3
2 2 / 2 \ 4*cot (4*x)*atan(2*x)
atan (2*x)*cot (4*x)*\-12 - 12*cot (4*x)/ + ---------------------
2
1 + 4*x
$$\left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)} + \frac{4 \cot^{3}{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}$$
Segunda derivada
[src]
/ 2 / 2 \ \ | cot (4*x)*(-1 + 4*x*atan(2*x)) 2 / 2 \ / 2 \ 12*\1 + cot (4*x)/*atan(2*x)*cot(4*x)| 8*|- ------------------------------ + 12*atan (2*x)*\1 + cot (4*x)/*\1 + 2*cot (4*x)/ - -------------------------------------|*cot(4*x) | 2 2 | | / 2\ 1 + 4*x | \ \1 + 4*x / /
$$8 \left(12 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)} - \frac{12 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{\left(4 x \operatorname{atan}{\left(2 x \right)} - 1\right) \cot^{2}{\left(4 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \cot{\left(4 x \right)}$$
Tercera derivada
[src]
/ / 2 \ \ | 3 | 6*x 16*x *atan(2*x) | | | cot (4*x)*|-------- - --------------- + atan(2*x)| | | | 2 2 | / 2 \ 2 / 2 \ / 2 \ / 2 \ | | \1 + 4*x 1 + 4*x / 2 / 2 \ |/ 2 \ 4 2 / 2 \| 9*cot (4*x)*\1 + cot (4*x)/*(-1 + 4*x*atan(2*x)) 36*\1 + cot (4*x)/*\1 + 2*cot (4*x)/*atan(2*x)*cot(4*x)| 32*|- -------------------------------------------------- - 12*atan (2*x)*\1 + cot (4*x)/*\\1 + cot (4*x)/ + 2*cot (4*x) + 7*cot (4*x)*\1 + cot (4*x)// + ------------------------------------------------ + -------------------------------------------------------| | 2 2 2 | | / 2\ / 2\ 1 + 4*x | \ \1 + 4*x / \1 + 4*x / /
$$32 \left(- 12 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(\left(\cot^{2}{\left(4 x \right)} + 1\right)^{2} + 7 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)} + 2 \cot^{4}{\left(4 x \right)}\right) \operatorname{atan}^{2}{\left(2 x \right)} + \frac{36 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{9 \left(4 x \operatorname{atan}{\left(2 x \right)} - 1\right) \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)}}{\left(4 x^{2} + 1\right)^{2}} - \frac{\left(- \frac{16 x^{2} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{6 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \cot^{3}{\left(4 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right)$$
Gráfico