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=(arctg(cuatro x))^(4-11x^ dos)
- y es igual a (arctg(4x)) en el grado (4 menos 11x al cuadrado )
- y es igual a (arctg(cuatro x)) en el grado (4 menos 11x en el grado dos)
- y=(arctg(4x))(4-11x2)
- y=arctg4x4-11x2
- y=(arctg(4x))^(4-11x²)
- y=(arctg(4x)) en el grado (4-11x en el grado 2)
- y=arctg4x^4-11x^2
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Expresiones semejantes
- y=(arctg(4x))^(4+11x^2)
Derivada de y=(arctg(4x))^(4-11x^2)
Solución
Ha introducido
[src]
2
4 - 11*x
(atan(4*x))
$$\operatorname{atan}^{4 - 11 x^{2}}{\left(4 x \right)}$$
atan(4*x)^(4 - 11*x^2)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
2 / / 2\ \
4 - 11*x | 4*\4 - 11*x / |
(atan(4*x)) *|-22*x*log(atan(4*x)) + ---------------------|
| / 2\ |
\ \1 + 16*x /*atan(4*x)/
$$\left(- 22 x \log{\left(\operatorname{atan}{\left(4 x \right)} \right)} + \frac{4 \left(4 - 11 x^{2}\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right) \operatorname{atan}^{4 - 11 x^{2}}{\left(4 x \right)}$$
Segunda derivada
[src]
/ 2 \
2 | / / 2\ \ / 2\ / 2\ |
4 - 11*x | | 2*\-4 + 11*x / | 88*x 8*\-4 + 11*x / 64*x*\-4 + 11*x / |
2*(atan(4*x)) *|-11*log(atan(4*x)) + 2*|11*x*log(atan(4*x)) + ---------------------| - --------------------- + ----------------------- + ----------------------|
| | / 2\ | / 2\ 2 2 |
| \ \1 + 16*x /*atan(4*x)/ \1 + 16*x /*atan(4*x) / 2\ 2 / 2\ |
\ \1 + 16*x / *atan (4*x) \1 + 16*x / *atan(4*x)/
$$2 \left(\frac{64 x \left(11 x^{2} - 4\right)}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} - \frac{88 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + \frac{8 \left(11 x^{2} - 4\right)}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(4 x \right)}} + 2 \left(11 x \log{\left(\operatorname{atan}{\left(4 x \right)} \right)} + \frac{2 \left(11 x^{2} - 4\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right)^{2} - 11 \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right) \operatorname{atan}^{4 - 11 x^{2}}{\left(4 x \right)}$$
Tercera derivada
[src]
/ / 2 / 2\ / 2\ 2 / 2\ / 2\ \\
| | 1056*x 16*\-4 + 11*x / 132*x 16*\-4 + 11*x / 1024*x *\-4 + 11*x / 192*x*\-4 + 11*x / ||
| 2*|33 - --------- - --------------- - --------------------- + ----------------------- + -------------------- + ----------------------||
| 3 | 2 2 / 2\ 2 2 2 ||
2 | / / 2\ \ / / 2\ \ / / 2\ / 2\ \ | 1 + 16*x 1 + 16*x \1 + 16*x /*atan(4*x) / 2\ 2 / 2\ / 2\ ||
4 - 11*x | | 2*\-4 + 11*x / | | 2*\-4 + 11*x / | | 88*x 8*\-4 + 11*x / 64*x*\-4 + 11*x / | \ \1 + 16*x / *atan (4*x) \1 + 16*x / \1 + 16*x / *atan(4*x)/|
-4*(atan(4*x)) *|2*|11*x*log(atan(4*x)) + ---------------------| + 3*|11*x*log(atan(4*x)) + ---------------------|*|-11*log(atan(4*x)) - --------------------- + ----------------------- + ----------------------| + --------------------------------------------------------------------------------------------------------------------------------------|
| | / 2\ | | / 2\ | | / 2\ 2 2 | / 2\ |
| \ \1 + 16*x /*atan(4*x)/ \ \1 + 16*x /*atan(4*x)/ | \1 + 16*x /*atan(4*x) / 2\ 2 / 2\ | \1 + 16*x /*atan(4*x) |
\ \ \1 + 16*x / *atan (4*x) \1 + 16*x / *atan(4*x)/ /
$$- 4 \left(2 \left(11 x \log{\left(\operatorname{atan}{\left(4 x \right)} \right)} + \frac{2 \left(11 x^{2} - 4\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right)^{3} + 3 \left(11 x \log{\left(\operatorname{atan}{\left(4 x \right)} \right)} + \frac{2 \left(11 x^{2} - 4\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right) \left(\frac{64 x \left(11 x^{2} - 4\right)}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} - \frac{88 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + \frac{8 \left(11 x^{2} - 4\right)}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(4 x \right)}} - 11 \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right) + \frac{2 \left(\frac{1024 x^{2} \left(11 x^{2} - 4\right)}{\left(16 x^{2} + 1\right)^{2}} - \frac{1056 x^{2}}{16 x^{2} + 1} + \frac{192 x \left(11 x^{2} - 4\right)}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} - \frac{132 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - \frac{16 \left(11 x^{2} - 4\right)}{16 x^{2} + 1} + \frac{16 \left(11 x^{2} - 4\right)}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(4 x \right)}} + 33\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right) \operatorname{atan}^{4 - 11 x^{2}}{\left(4 x \right)}$$
Gráfico