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:
-
Derivada de sin(2*x+3)
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Derivada de 2/e^x
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Derivada de e^(2*cos(t)^(2)-2*sin(t)^(2))
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Derivada de (1-2*x)^3
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Expresiones idénticas
- y=((arctg(4x)))^(x)^ dos
- y es igual a ((arctg(4x))) en el grado (x) al cuadrado
- y es igual a ((arctg(4x))) en el grado (x) en el grado dos
- y=((arctg(4x)))(x)2
- y=arctg4xx2
- y=((arctg(4x)))^(x)²
- y=((arctg(4x))) en el grado (x) en el grado 2
- y=arctg4x^x^2
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Expresiones con funciones
- arctg
- arctg^2(1/x)
- arctg(x+cosx)
Derivada de y=((arctg(4x)))^(x)^2
Solución
Ha introducido
[src]
/ 2\
\x /
(atan(4*x))
$$\operatorname{atan}^{x^{2}}{\left(4 x \right)}$$
atan(4*x)^(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 \
\x / | 4*x |
(atan(4*x)) *|2*x*log(atan(4*x)) + ---------------------|
| / 2\ |
\ \1 + 16*x /*atan(4*x)/
$$\left(\frac{4 x^{2}}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + 2 x \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right) \operatorname{atan}^{x^{2}}{\left(4 x \right)}$$
Segunda derivada
[src]
/ 2\ / 2 3 2 \
\x / | 2 / 2*x \ 64*x 8*x 8*x |
2*(atan(4*x)) *|2*x *|--------------------- + log(atan(4*x))| - ---------------------- - ----------------------- + --------------------- + log(atan(4*x))|
| |/ 2\ | 2 2 / 2\ |
| \\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) /
$$2 \left(- \frac{64 x^{3}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + 2 x^{2} \left(\frac{2 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right)^{2} - \frac{8 x^{2}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(4 x \right)}} + \frac{8 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right) \operatorname{atan}^{x^{2}}{\left(4 x \right)}$$
Tercera derivada
[src]
/ / 2 4 2 3 \\
| | 112*x 1024*x 12*x 16*x 192*x ||
| 2*|3 - --------- + ------------ - --------------------- + ----------------------- + ----------------------||
| | 2 2 / 2\ 2 2 ||
/ 2\ | 3 / 2 3 \ | 1 + 16*x / 2\ \1 + 16*x /*atan(4*x) / 2\ 2 / 2\ ||
\x / | 3 / 2*x \ / 2*x \ | 8*x 8*x 64*x | \ \1 + 16*x / \1 + 16*x / *atan (4*x) \1 + 16*x / *atan(4*x)/|
4*(atan(4*x)) *|2*x *|--------------------- + log(atan(4*x))| - 3*x*|--------------------- + log(atan(4*x))|*|-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)/ /
$$4 \left(2 x^{3} \left(\frac{2 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right)^{3} - 3 x \left(\frac{2 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right) \left(\frac{64 x^{3}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + \frac{8 x^{2}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(4 x \right)}} - \frac{8 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - \log{\left(\operatorname{atan}{\left(4 x \right)} \right)}\right) + \frac{2 \left(\frac{1024 x^{4}}{\left(16 x^{2} + 1\right)^{2}} + \frac{192 x^{3}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} - \frac{112 x^{2}}{16 x^{2} + 1} + \frac{16 x^{2}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(4 x \right)}} - \frac{12 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} + 3\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right) \operatorname{atan}^{x^{2}}{\left(4 x \right)}$$
Gráfico