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^-1
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Derivada de (x^2)'
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Derivada de y
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Derivada de 16/x
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Expresiones idénticas
- y=ctg^3x*arctg^3x
- y es igual a ctg al cubo x multiplicar por arctg al cubo x
- y=ctg3x*arctg3x
- y=ctg³x*arctg³x
- y=ctg en el grado 3x*arctg en el grado 3x
- y=ctg^3xarctg^3x
- y=ctg3xarctg3x
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Expresiones con funciones
- ctg
- ctg(1/x)
- ctg4x
- ctg(2x+1)
- ctg3x*arccos(3x)^2
- ctg(x^2)
- arctg
- arctg1/x
- arctg(2x)
- arctg^3*4x*3^sinx
- arctg(sqrt(x))
- arctg(cos(x))
Derivada de y=ctg^3x*arctg^3x
Solución
Ha introducido
[src]
3 3 cot (x)*atan (x)
$$\cot^{3}{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)}$$
cot(x)^3*atan(x)^3
Primera derivada
[src]
2 3
3 2 / 2 \ 3*atan (x)*cot (x)
atan (x)*cot (x)*\-3 - 3*cot (x)/ + ------------------
2
1 + x
$$\left(- 3 \cot^{2}{\left(x \right)} - 3\right) \cot^{2}{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)} + \frac{3 \cot^{3}{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1}$$
Segunda derivada
[src]
/ 2 / 2 \ \ | 2 / 2 \ / 2 \ cot (x)*(-1 + x*atan(x)) 3*\1 + cot (x)/*atan(x)*cot(x)| 6*|atan (x)*\1 + cot (x)/*\1 + 2*cot (x)/ - ------------------------ - ------------------------------|*atan(x)*cot(x) | 2 2 | | / 2\ 1 + x | \ \1 + x / /
$$6 \left(\left(\cot^{2}{\left(x \right)} + 1\right) \left(2 \cot^{2}{\left(x \right)} + 1\right) \operatorname{atan}^{2}{\left(x \right)} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{\left(x \operatorname{atan}{\left(x \right)} - 1\right) \cot^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \cot{\left(x \right)} \operatorname{atan}{\left(x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \ | 3 | 1 2 6*x*atan(x) 4*x *atan (x)| | |cot (x)*|------ - atan (x) - ----------- + -------------| | | | 2 2 2 | / 2 \ 2 / 2 \ / 2 \ 2 / 2 \ | | \1 + x 1 + x 1 + x / 3 / 2 \ |/ 2 \ 4 2 / 2 \| 9*atan (x)*\1 + cot (x)/*\1 + 2*cot (x)/*cot(x) 9*cot (x)*\1 + cot (x)/*(-1 + x*atan(x))*atan(x)| 6*|--------------------------------------------------------- - atan (x)*\1 + cot (x)/*\\1 + cot (x)/ + 2*cot (x) + 7*cot (x)*\1 + cot (x)// + ----------------------------------------------- + ------------------------------------------------| | 2 2 2 | | / 2\ 1 + x / 2\ | \ \1 + x / \1 + x / /
$$6 \left(- \left(\cot^{2}{\left(x \right)} + 1\right) \left(\left(\cot^{2}{\left(x \right)} + 1\right)^{2} + 7 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} + 2 \cot^{4}{\left(x \right)}\right) \operatorname{atan}^{3}{\left(x \right)} + \frac{9 \left(\cot^{2}{\left(x \right)} + 1\right) \left(2 \cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{9 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right) \cot^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)$$
Gráfico