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