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 (-4)/x^2
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Derivada de 2/x²
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Derivada de -2*y
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Derivada de (3+2x)/(x-5)
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Expresiones idénticas
- y=(uno +x^ dos)^arctg(2x)
- y es igual a (1 más x al cuadrado ) en el grado arctg(2x)
- y es igual a (uno más x en el grado dos) en el grado arctg(2x)
- y=(1+x2)arctg(2x)
- y=1+x2arctg2x
- y=(1+x²)^arctg(2x)
- y=(1+x en el grado 2) en el grado arctg(2x)
- y=1+x^2^arctg2x
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Expresiones semejantes
- y=(1-x^2)^arctg(2x)
Derivada de y=(1+x^2)^arctg(2x)
Solución
Ha introducido
[src]
atan(2*x) / 2\ \1 + x /
$$\left(x^{2} + 1\right)^{\operatorname{atan}{\left(2 x \right)}}$$
(1 + x^2)^atan(2*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
atan(2*x) / / 2\ \
/ 2\ |2*log\1 + x / 2*x*atan(2*x)|
\1 + x / *|------------- + -------------|
| 2 2 |
\ 1 + 4*x 1 + x /
$$\left(x^{2} + 1\right)^{\operatorname{atan}{\left(2 x \right)}} \left(\frac{2 x \operatorname{atan}{\left(2 x \right)}}{x^{2} + 1} + \frac{2 \log{\left(x^{2} + 1 \right)}}{4 x^{2} + 1}\right)$$
Segunda derivada
[src]
/ 2 \
atan(2*x) | / / 2\ \ / 2\ 2 |
/ 2\ | |log\1 + x / x*atan(2*x)| atan(2*x) 8*x*log\1 + x / 2*x *atan(2*x) 4*x |
2*\1 + x / *|2*|----------- + -----------| + --------- - --------------- - -------------- + -------------------|
| | 2 2 | 2 2 2 / 2\ / 2\|
| \ 1 + 4*x 1 + x / 1 + x / 2\ / 2\ \1 + x /*\1 + 4*x /|
\ \1 + 4*x / \1 + x / /
$$2 \left(x^{2} + 1\right)^{\operatorname{atan}{\left(2 x \right)}} \left(- \frac{2 x^{2} \operatorname{atan}{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{8 x \log{\left(x^{2} + 1 \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{4 x}{\left(x^{2} + 1\right) \left(4 x^{2} + 1\right)} + 2 \left(\frac{x \operatorname{atan}{\left(2 x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{4 x^{2} + 1}\right)^{2} + \frac{\operatorname{atan}{\left(2 x \right)}}{x^{2} + 1}\right)$$
3-я производная
[src]
/ 3 \
atan(2*x) | / / 2\ \ / 2\ / / 2\ \ / 2 / 2\\ 2 2 3 2 / 2\|
/ 2\ | |log\1 + x / x*atan(2*x)| 4*log\1 + x / |log\1 + x / x*atan(2*x)| | atan(2*x) 4*x 2*x *atan(2*x) 8*x*log\1 + x /| 3 24*x 6*x 3*x*atan(2*x) 4*x *atan(2*x) 64*x *log\1 + x /|
4*\1 + x / *|2*|----------- + -----------| - ------------- - 3*|----------- + -----------|*|- --------- - ------------------- + -------------- + ---------------| + ------------------- - -------------------- - -------------------- - ------------- + -------------- + -----------------|
| | 2 2 | 2 | 2 2 | | 2 / 2\ / 2\ 2 2 | / 2\ / 2\ 2 2 2 3 3 |
| \ 1 + 4*x 1 + x / / 2\ \ 1 + 4*x 1 + x / | 1 + x \1 + x /*\1 + 4*x / / 2\ / 2\ | \1 + x /*\1 + 4*x / / 2\ / 2\ / 2\ / 2\ / 2\ / 2\ / 2\ |
\ \1 + 4*x / \ \1 + x / \1 + 4*x / / \1 + x /*\1 + 4*x / \1 + x / *\1 + 4*x / \1 + x / \1 + x / \1 + 4*x / /
$$4 \left(x^{2} + 1\right)^{\operatorname{atan}{\left(2 x \right)}} \left(\frac{4 x^{3} \operatorname{atan}{\left(2 x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{64 x^{2} \log{\left(x^{2} + 1 \right)}}{\left(4 x^{2} + 1\right)^{3}} - \frac{24 x^{2}}{\left(x^{2} + 1\right) \left(4 x^{2} + 1\right)^{2}} - \frac{6 x^{2}}{\left(x^{2} + 1\right)^{2} \left(4 x^{2} + 1\right)} - \frac{3 x \operatorname{atan}{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + 2 \left(\frac{x \operatorname{atan}{\left(2 x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{4 x^{2} + 1}\right)^{3} - 3 \left(\frac{x \operatorname{atan}{\left(2 x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{4 x^{2} + 1}\right) \left(\frac{2 x^{2} \operatorname{atan}{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{8 x \log{\left(x^{2} + 1 \right)}}{\left(4 x^{2} + 1\right)^{2}} - \frac{4 x}{\left(x^{2} + 1\right) \left(4 x^{2} + 1\right)} - \frac{\operatorname{atan}{\left(2 x \right)}}{x^{2} + 1}\right) - \frac{4 \log{\left(x^{2} + 1 \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{3}{\left(x^{2} + 1\right) \left(4 x^{2} + 1\right)}\right)$$
Tercera derivada
[src]
/ 3 \
atan(2*x) | / / 2\ \ / 2\ / / 2\ \ / 2 / 2\\ 2 2 3 2 / 2\|
/ 2\ | |log\1 + x / x*atan(2*x)| 4*log\1 + x / |log\1 + x / x*atan(2*x)| | atan(2*x) 4*x 2*x *atan(2*x) 8*x*log\1 + x /| 3 24*x 6*x 3*x*atan(2*x) 4*x *atan(2*x) 64*x *log\1 + x /|
4*\1 + x / *|2*|----------- + -----------| - ------------- - 3*|----------- + -----------|*|- --------- - ------------------- + -------------- + ---------------| + ------------------- - -------------------- - -------------------- - ------------- + -------------- + -----------------|
| | 2 2 | 2 | 2 2 | | 2 / 2\ / 2\ 2 2 | / 2\ / 2\ 2 2 2 3 3 |
| \ 1 + 4*x 1 + x / / 2\ \ 1 + 4*x 1 + x / | 1 + x \1 + x /*\1 + 4*x / / 2\ / 2\ | \1 + x /*\1 + 4*x / / 2\ / 2\ / 2\ / 2\ / 2\ / 2\ / 2\ |
\ \1 + 4*x / \ \1 + x / \1 + 4*x / / \1 + x /*\1 + 4*x / \1 + x / *\1 + 4*x / \1 + x / \1 + x / \1 + 4*x / /
$$4 \left(x^{2} + 1\right)^{\operatorname{atan}{\left(2 x \right)}} \left(\frac{4 x^{3} \operatorname{atan}{\left(2 x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{64 x^{2} \log{\left(x^{2} + 1 \right)}}{\left(4 x^{2} + 1\right)^{3}} - \frac{24 x^{2}}{\left(x^{2} + 1\right) \left(4 x^{2} + 1\right)^{2}} - \frac{6 x^{2}}{\left(x^{2} + 1\right)^{2} \left(4 x^{2} + 1\right)} - \frac{3 x \operatorname{atan}{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + 2 \left(\frac{x \operatorname{atan}{\left(2 x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{4 x^{2} + 1}\right)^{3} - 3 \left(\frac{x \operatorname{atan}{\left(2 x \right)}}{x^{2} + 1} + \frac{\log{\left(x^{2} + 1 \right)}}{4 x^{2} + 1}\right) \left(\frac{2 x^{2} \operatorname{atan}{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{8 x \log{\left(x^{2} + 1 \right)}}{\left(4 x^{2} + 1\right)^{2}} - \frac{4 x}{\left(x^{2} + 1\right) \left(4 x^{2} + 1\right)} - \frac{\operatorname{atan}{\left(2 x \right)}}{x^{2} + 1}\right) - \frac{4 \log{\left(x^{2} + 1 \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{3}{\left(x^{2} + 1\right) \left(4 x^{2} + 1\right)}\right)$$
Gráfico