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 (-1)/x-3*x
- Derivada de y=ax
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Expresiones idénticas
- y=(arcsin3x)^(ln(x+ uno))
- y es igual a (arc seno de 3x) en el grado (ln(x más 1))
- y es igual a (arc seno de 3x) en el grado (ln(x más uno))
- y=(arcsin3x)(ln(x+1))
- y=arcsin3xlnx+1
- y=arcsin3x^lnx+1
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Expresiones semejantes
- y=(arcsin3x)^(ln(x-1))
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Expresiones con funciones
- ln
- ln(x+10)^11
- ln((x^2)-1)
- ln3x^5
- ln^3(x^2+1)
- ln(1+|x|)
Derivada de y=(arcsin3x)^(ln(x+1))
Solución
Ha introducido
[src]
log(x + 1) asin (3*x)
$$\operatorname{asin}^{\log{\left(x + 1 \right)}}{\left(3 x \right)}$$
asin(3*x)^log(x + 1)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
Primera derivada
[src]
log(x + 1) /log(asin(3*x)) 3*log(x + 1) \
asin (3*x)*|-------------- + -----------------------|
| x + 1 __________ |
| / 2 |
\ \/ 1 - 9*x *asin(3*x)/
$$\left(\frac{\log{\left(\operatorname{asin}{\left(3 x \right)} \right)}}{x + 1} + \frac{3 \log{\left(x + 1 \right)}}{\sqrt{1 - 9 x^{2}} \operatorname{asin}{\left(3 x \right)}}\right) \operatorname{asin}^{\log{\left(x + 1 \right)}}{\left(3 x \right)}$$
Segunda derivada
[src]
/ 2 \
log(1 + x) |/log(asin(3*x)) 3*log(1 + x) \ log(asin(3*x)) 6 9*log(1 + x) 27*x*log(1 + x) |
asin (3*x)*||-------------- + -----------------------| - -------------- + ------------------------------- + ---------------------- + -----------------------|
|| 1 + x __________ | 2 __________ / 2\ 2 3/2 |
|| / 2 | (1 + x) / 2 \-1 + 9*x /*asin (3*x) / 2\ |
\\ \/ 1 - 9*x *asin(3*x)/ (1 + x)*\/ 1 - 9*x *asin(3*x) \1 - 9*x / *asin(3*x)/
$$\left(\frac{27 x \log{\left(x + 1 \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(3 x \right)}} + \left(\frac{\log{\left(\operatorname{asin}{\left(3 x \right)} \right)}}{x + 1} + \frac{3 \log{\left(x + 1 \right)}}{\sqrt{1 - 9 x^{2}} \operatorname{asin}{\left(3 x \right)}}\right)^{2} + \frac{9 \log{\left(x + 1 \right)}}{\left(9 x^{2} - 1\right) \operatorname{asin}^{2}{\left(3 x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(3 x \right)} \right)}}{\left(x + 1\right)^{2}} + \frac{6}{\sqrt{1 - 9 x^{2}} \left(x + 1\right) \operatorname{asin}{\left(3 x \right)}}\right) \operatorname{asin}^{\log{\left(x + 1 \right)}}{\left(3 x \right)}$$
Tercera derivada
[src]
/ 3 2 \
log(1 + x) |/log(asin(3*x)) 3*log(1 + x) \ 2*log(asin(3*x)) /log(asin(3*x)) 3*log(1 + x) \ / log(asin(3*x)) 6 9*log(1 + x) 27*x*log(1 + x) \ 9 27 27*log(1 + x) 54*log(1 + x) 243*x*log(1 + x) 81*x 729*x *log(1 + x) |
asin (3*x)*||-------------- + -----------------------| + ---------------- + 3*|-------------- + -----------------------|*|- -------------- + ------------------------------- + ---------------------- + -----------------------| - -------------------------------- + ------------------------------ + ----------------------- + ------------------------ - ----------------------- + ------------------------------- + -----------------------|
|| 1 + x __________ | 3 | 1 + x __________ | | 2 __________ / 2\ 2 3/2 | __________ / 2\ 2 3/2 3/2 2 3/2 5/2 |
|| / 2 | (1 + x) | / 2 | | (1 + x) / 2 \-1 + 9*x /*asin (3*x) / 2\ | 2 / 2 (1 + x)*\-1 + 9*x /*asin (3*x) / 2\ / 2\ 3 / 2\ 2 / 2\ / 2\ |
\\ \/ 1 - 9*x *asin(3*x)/ \ \/ 1 - 9*x *asin(3*x)/ \ (1 + x)*\/ 1 - 9*x *asin(3*x) \1 - 9*x / *asin(3*x)/ (1 + x) *\/ 1 - 9*x *asin(3*x) \1 - 9*x / *asin(3*x) \1 - 9*x / *asin (3*x) \-1 + 9*x / *asin (3*x) (1 + x)*\1 - 9*x / *asin(3*x) \1 - 9*x / *asin(3*x)/
$$\left(\frac{729 x^{2} \log{\left(x + 1 \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(3 x \right)}} - \frac{243 x \log{\left(x + 1 \right)}}{\left(9 x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(3 x \right)}} + \frac{81 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \left(x + 1\right) \operatorname{asin}{\left(3 x \right)}} + \left(\frac{\log{\left(\operatorname{asin}{\left(3 x \right)} \right)}}{x + 1} + \frac{3 \log{\left(x + 1 \right)}}{\sqrt{1 - 9 x^{2}} \operatorname{asin}{\left(3 x \right)}}\right)^{3} + 3 \left(\frac{\log{\left(\operatorname{asin}{\left(3 x \right)} \right)}}{x + 1} + \frac{3 \log{\left(x + 1 \right)}}{\sqrt{1 - 9 x^{2}} \operatorname{asin}{\left(3 x \right)}}\right) \left(\frac{27 x \log{\left(x + 1 \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(3 x \right)}} + \frac{9 \log{\left(x + 1 \right)}}{\left(9 x^{2} - 1\right) \operatorname{asin}^{2}{\left(3 x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(3 x \right)} \right)}}{\left(x + 1\right)^{2}} + \frac{6}{\sqrt{1 - 9 x^{2}} \left(x + 1\right) \operatorname{asin}{\left(3 x \right)}}\right) + \frac{27}{\left(x + 1\right) \left(9 x^{2} - 1\right) \operatorname{asin}^{2}{\left(3 x \right)}} + \frac{2 \log{\left(\operatorname{asin}{\left(3 x \right)} \right)}}{\left(x + 1\right)^{3}} - \frac{9}{\sqrt{1 - 9 x^{2}} \left(x + 1\right)^{2} \operatorname{asin}{\left(3 x \right)}} + \frac{27 \log{\left(x + 1 \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(3 x \right)}} + \frac{54 \log{\left(x + 1 \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(3 x \right)}}\right) \operatorname{asin}^{\log{\left(x + 1 \right)}}{\left(3 x \right)}$$
Gráfico