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
-
¿Cómo usar?
- Derivada de:
-
Derivada de x^4/3-x
-
Derivada de x^-4/5
-
Derivada de x=1
-
Derivada de x^2*2^x
-
Expresiones idénticas
- y=(arcsin2x)^(ln(x+ tres))
- y es igual a (arc seno de 2x) en el grado (ln(x más 3))
- y es igual a (arc seno de 2x) en el grado (ln(x más tres))
- y=(arcsin2x)(ln(x+3))
- y=arcsin2xlnx+3
- y=arcsin2x^lnx+3
-
Expresiones semejantes
- y=(arcsin2x)^(ln(x-3))
Derivada de y=(arcsin2x)^(ln(x+3))
Solución
Ha introducido
[src]
log(x + 3) asin (2*x)
$$\operatorname{asin}^{\log{\left(x + 3 \right)}}{\left(2 x \right)}$$
asin(2*x)^log(x + 3)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
-
Simplificamos:
Respuesta:
Primera derivada
[src]
log(x + 3) /log(asin(2*x)) 2*log(x + 3) \
asin (2*x)*|-------------- + -----------------------|
| x + 3 __________ |
| / 2 |
\ \/ 1 - 4*x *asin(2*x)/
$$\left(\frac{\log{\left(\operatorname{asin}{\left(2 x \right)} \right)}}{x + 3} + \frac{2 \log{\left(x + 3 \right)}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}\right) \operatorname{asin}^{\log{\left(x + 3 \right)}}{\left(2 x \right)}$$
Segunda derivada
[src]
/ 2 \
log(3 + x) |/log(asin(2*x)) 2*log(3 + x) \ log(asin(2*x)) 4 4*log(3 + x) 8*x*log(3 + x) |
asin (2*x)*||-------------- + -----------------------| - -------------- + ------------------------------- + ---------------------- + -----------------------|
|| 3 + x __________ | 2 __________ / 2\ 2 3/2 |
|| / 2 | (3 + x) / 2 \-1 + 4*x /*asin (2*x) / 2\ |
\\ \/ 1 - 4*x *asin(2*x)/ \/ 1 - 4*x *(3 + x)*asin(2*x) \1 - 4*x / *asin(2*x)/
$$\left(\frac{8 x \log{\left(x + 3 \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(2 x \right)}} + \left(\frac{\log{\left(\operatorname{asin}{\left(2 x \right)} \right)}}{x + 3} + \frac{2 \log{\left(x + 3 \right)}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}\right)^{2} + \frac{4 \log{\left(x + 3 \right)}}{\left(4 x^{2} - 1\right) \operatorname{asin}^{2}{\left(2 x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(2 x \right)} \right)}}{\left(x + 3\right)^{2}} + \frac{4}{\sqrt{1 - 4 x^{2}} \left(x + 3\right) \operatorname{asin}{\left(2 x \right)}}\right) \operatorname{asin}^{\log{\left(x + 3 \right)}}{\left(2 x \right)}$$
Tercera derivada
[src]
/ 3 2 \
log(3 + x) |/log(asin(2*x)) 2*log(3 + x) \ 2*log(asin(2*x)) /log(asin(2*x)) 2*log(3 + x) \ / log(asin(2*x)) 4 4*log(3 + x) 8*x*log(3 + x) \ 6 8*log(3 + x) 12 16*log(3 + x) 48*x*log(3 + x) 24*x 96*x *log(3 + x) |
asin (2*x)*||-------------- + -----------------------| + ---------------- + 3*|-------------- + -----------------------|*|- -------------- + ------------------------------- + ---------------------- + -----------------------| - -------------------------------- + ----------------------- + ------------------------------ + ------------------------ - ----------------------- + ------------------------------- + -----------------------|
|| 3 + x __________ | 3 | 3 + x __________ | | 2 __________ / 2\ 2 3/2 | __________ 3/2 / 2\ 2 3/2 2 3/2 5/2 |
|| / 2 | (3 + x) | / 2 | | (3 + x) / 2 \-1 + 4*x /*asin (2*x) / 2\ | / 2 2 / 2\ \-1 + 4*x /*(3 + x)*asin (2*x) / 2\ 3 / 2\ 2 / 2\ / 2\ |
\\ \/ 1 - 4*x *asin(2*x)/ \ \/ 1 - 4*x *asin(2*x)/ \ \/ 1 - 4*x *(3 + x)*asin(2*x) \1 - 4*x / *asin(2*x)/ \/ 1 - 4*x *(3 + x) *asin(2*x) \1 - 4*x / *asin(2*x) \1 - 4*x / *asin (2*x) \-1 + 4*x / *asin (2*x) \1 - 4*x / *(3 + x)*asin(2*x) \1 - 4*x / *asin(2*x)/
$$\left(\frac{96 x^{2} \log{\left(x + 3 \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(2 x \right)}} - \frac{48 x \log{\left(x + 3 \right)}}{\left(4 x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(2 x \right)}} + \frac{24 x}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \left(x + 3\right) \operatorname{asin}{\left(2 x \right)}} + \left(\frac{\log{\left(\operatorname{asin}{\left(2 x \right)} \right)}}{x + 3} + \frac{2 \log{\left(x + 3 \right)}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}\right)^{3} + 3 \left(\frac{\log{\left(\operatorname{asin}{\left(2 x \right)} \right)}}{x + 3} + \frac{2 \log{\left(x + 3 \right)}}{\sqrt{1 - 4 x^{2}} \operatorname{asin}{\left(2 x \right)}}\right) \left(\frac{8 x \log{\left(x + 3 \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(2 x \right)}} + \frac{4 \log{\left(x + 3 \right)}}{\left(4 x^{2} - 1\right) \operatorname{asin}^{2}{\left(2 x \right)}} - \frac{\log{\left(\operatorname{asin}{\left(2 x \right)} \right)}}{\left(x + 3\right)^{2}} + \frac{4}{\sqrt{1 - 4 x^{2}} \left(x + 3\right) \operatorname{asin}{\left(2 x \right)}}\right) + \frac{12}{\left(x + 3\right) \left(4 x^{2} - 1\right) \operatorname{asin}^{2}{\left(2 x \right)}} + \frac{2 \log{\left(\operatorname{asin}{\left(2 x \right)} \right)}}{\left(x + 3\right)^{3}} - \frac{6}{\sqrt{1 - 4 x^{2}} \left(x + 3\right)^{2} \operatorname{asin}{\left(2 x \right)}} + \frac{8 \log{\left(x + 3 \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(2 x \right)}} + \frac{16 \log{\left(x + 3 \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(2 x \right)}}\right) \operatorname{asin}^{\log{\left(x + 3 \right)}}{\left(2 x \right)}$$
Gráfico