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 x^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de y=-6/x
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Expresiones idénticas
- y=ctg^ tres (4x)*arctg(2x)^ tres
- y es igual a ctg al cubo (4x) multiplicar por arctg(2x) al cubo
- y es igual a ctg en el grado tres (4x) multiplicar por arctg(2x) en el grado tres
- y=ctg3(4x)*arctg(2x)3
- y=ctg34x*arctg2x3
- y=ctg³(4x)*arctg(2x)³
- y=ctg en el grado 3(4x)*arctg(2x) en el grado 3
- y=ctg^3(4x)arctg(2x)^3
- y=ctg3(4x)arctg(2x)3
- y=ctg34xarctg2x3
- y=ctg^34xarctg2x^3
Derivada de y=ctg^3(4x)*arctg(2x)^3
Solución
Ha introducido
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3 3 cot (4*x)*atan (2*x)
$$\cot^{3}{\left(4 x \right)} \operatorname{atan}^{3}{\left(2 x \right)}$$
cot(4*x)^3*atan(2*x)^3
Primera derivada
[src]
2 3
3 2 / 2 \ 6*atan (2*x)*cot (4*x)
atan (2*x)*cot (4*x)*\-12 - 12*cot (4*x)/ + ----------------------
2
1 + 4*x
$$\left(- 12 \cot^{2}{\left(4 x \right)} - 12\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + \frac{6 \cot^{3}{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1}$$
Segunda derivada
[src]
/ 2 / 2 \ \ | cot (4*x)*(-1 + 2*x*atan(2*x)) 2 / 2 \ / 2 \ 6*\1 + cot (4*x)/*atan(2*x)*cot(4*x)| 24*|- ------------------------------ + 4*atan (2*x)*\1 + cot (4*x)/*\1 + 2*cot (4*x)/ - ------------------------------------|*atan(2*x)*cot(4*x) | 2 2 | | / 2\ 1 + 4*x | \ \1 + 4*x / /
$$24 \left(4 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)} - \frac{6 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{\left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \cot^{2}{\left(4 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \cot{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \ | 3 | 1 2 12*x*atan(2*x) 16*x *atan (2*x)| | |cot (4*x)*|-------- - atan (2*x) - -------------- + ----------------| | | | 2 2 2 | / 2 \ 2 / 2 \ 2 / 2 \ / 2 \ | | \1 + 4*x 1 + 4*x 1 + 4*x / 3 / 2 \ |/ 2 \ 4 2 / 2 \| 18*cot (4*x)*\1 + cot (4*x)/*(-1 + 2*x*atan(2*x))*atan(2*x) 36*atan (2*x)*\1 + cot (4*x)/*\1 + 2*cot (4*x)/*cot(4*x)| 48*|--------------------------------------------------------------------- - 8*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 / /
$$48 \left(- 8 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(\left(\cot^{2}{\left(4 x \right)} + 1\right)^{2} + 7 \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)} + 2 \cot^{4}{\left(4 x \right)}\right) \operatorname{atan}^{3}{\left(2 x \right)} + \frac{36 \left(\cot^{2}{\left(4 x \right)} + 1\right) \left(2 \cot^{2}{\left(4 x \right)} + 1\right) \cot{\left(4 x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{18 \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \left(\cot^{2}{\left(4 x \right)} + 1\right) \cot^{2}{\left(4 x \right)} \operatorname{atan}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{\left(\frac{16 x^{2} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{atan}^{2}{\left(2 x \right)} + \frac{1}{4 x^{2} + 1}\right) \cot^{3}{\left(4 x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right)$$
Gráfico