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*e
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Derivada de -2x
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Derivada de e^-1
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Derivada de 8/x
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Expresiones idénticas
- y=(arctan3x)^ln
- y es igual a (arc tangente de 3x) en el grado ln
- y=(arctan3x)ln
- y=arctan3xln
- y=arctan3x^ln
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Expresiones con funciones
- ln
- ln(x/2)
- ln((x+1)/(x-1))
- ln^2x
- ln(x)+x
- ln(x-3)
Derivada de y=(arctan3x)^ln
Solución
Ha introducido
[src]
log(x) atan (3*x)
$$\operatorname{atan}^{\log{\left(x \right)}}{\left(3 x \right)}$$
atan(3*x)^log(x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
log(x) /log(atan(3*x)) 3*log(x) \
atan (3*x)*|-------------- + --------------------|
| x / 2\ |
\ \1 + 9*x /*atan(3*x)/
$$\left(\frac{3 \log{\left(x \right)}}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(3 x \right)}$$
Segunda derivada
[src]
/ 2 \
log(x) |/log(atan(3*x)) 3*log(x) \ log(atan(3*x)) 9*log(x) 6 54*x*log(x) |
atan (3*x)*||-------------- + --------------------| - -------------- - ---------------------- + ---------------------- - ---------------------|
|| x / 2\ | 2 2 / 2\ 2 |
|\ \1 + 9*x /*atan(3*x)/ x / 2\ 2 x*\1 + 9*x /*atan(3*x) / 2\ |
\ \1 + 9*x / *atan (3*x) \1 + 9*x / *atan(3*x)/
$$\left(- \frac{54 x \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + \left(\frac{3 \log{\left(x \right)}}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x}\right)^{2} - \frac{9 \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(3 x \right)}} + \frac{6}{x \left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x^{2}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(3 x \right)}$$
Tercera derivada
[src]
/ 3 2 \
log(x) |/log(atan(3*x)) 3*log(x) \ 162 /log(atan(3*x)) 3*log(x) \ /log(atan(3*x)) 6 9*log(x) 54*x*log(x) \ 2*log(atan(3*x)) 54*log(x) 27 9 54*log(x) 486*x*log(x) 1944*x *log(x) |
atan (3*x)*||-------------- + --------------------| - --------------------- - 3*|-------------- + --------------------|*|-------------- - ---------------------- + ---------------------- + ---------------------| + ---------------- - --------------------- - ------------------------ - ----------------------- + ---------------------- + ---------------------- + ---------------------|
|| x / 2\ | 2 | x / 2\ | | 2 / 2\ 2 2 | 3 2 2 2 / 2\ 3 3 3 |
|\ \1 + 9*x /*atan(3*x)/ / 2\ \ \1 + 9*x /*atan(3*x)/ | x x*\1 + 9*x /*atan(3*x) / 2\ 2 / 2\ | x / 2\ / 2\ 2 x *\1 + 9*x /*atan(3*x) / 2\ 3 / 2\ 2 / 2\ |
\ \1 + 9*x / *atan(3*x) \ \1 + 9*x / *atan (3*x) \1 + 9*x / *atan(3*x)/ \1 + 9*x / *atan(3*x) x*\1 + 9*x / *atan (3*x) \1 + 9*x / *atan (3*x) \1 + 9*x / *atan (3*x) \1 + 9*x / *atan(3*x)/
$$\left(\frac{1944 x^{2} \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{3} \operatorname{atan}{\left(3 x \right)}} + \frac{486 x \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(3 x \right)}} + \left(\frac{3 \log{\left(x \right)}}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{3 \log{\left(x \right)}}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x}\right) \left(\frac{54 x \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + \frac{9 \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(3 x \right)}} - \frac{6}{x \left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x^{2}}\right) - \frac{54 \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} - \frac{162}{\left(9 x^{2} + 1\right)^{2} \operatorname{atan}{\left(3 x \right)}} + \frac{54 \log{\left(x \right)}}{\left(9 x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(3 x \right)}} - \frac{27}{x \left(9 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(3 x \right)}} - \frac{9}{x^{2} \left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} + \frac{2 \log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{x^{3}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(3 x \right)}$$
Gráfico