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 e^-1
-
Derivada de (x^2)'
-
Derivada de y
-
Derivada de (x^5+1)
-
Expresiones idénticas
- y=(cos(3x))^arcsin(3x)
- y es igual a ( coseno de (3x)) en el grado arc seno de (3x)
- y=(cos(3x))arcsin(3x)
- y=cos3xarcsin3x
- y=cos3x^arcsin3x
-
Expresiones con funciones
- Coseno cos
- cos(x)/2
- cosx/lnx
- cos(x)^(1/2)
- cos(x)*log(x)
- cos(x)^(23)
- arcsin
- arcsin((x+1)/x)
- arcsin^26x
- arcsinsqrt(1-x^2)
- arcsin√(1-2*x)
- arcsin^2(sqrt(x))
Derivada de y=(cos(3x))^arcsin(3x)
Solución
Ha introducido
[src]
asin(3*x) cos (3*x)
$$\cos^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}$$
cos(3*x)^asin(3*x)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
asin(3*x) /3*log(cos(3*x)) 3*asin(3*x)*sin(3*x)\
cos (3*x)*|--------------- - --------------------|
| __________ cos(3*x) |
| / 2 |
\ \/ 1 - 9*x /
$$\left(- \frac{3 \sin{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos{\left(3 x \right)}} + \frac{3 \log{\left(\cos{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right) \cos^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}$$
Segunda derivada
[src]
/ 2 2 \
asin(3*x) |/ log(cos(3*x)) asin(3*x)*sin(3*x)\ sin (3*x)*asin(3*x) 2*sin(3*x) 3*x*log(cos(3*x))|
9*cos (3*x)*||- ------------- + ------------------| - asin(3*x) - ------------------- - ---------------------- + -----------------|
|| __________ cos(3*x) | 2 __________ 3/2 |
|| / 2 | cos (3*x) / 2 / 2\ |
\\ \/ 1 - 9*x / \/ 1 - 9*x *cos(3*x) \1 - 9*x / /
$$9 \left(\frac{3 x \log{\left(\cos{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\sin{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \frac{\log{\left(\cos{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right)^{2} - \frac{\sin^{2}{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} - \operatorname{asin}{\left(3 x \right)} - \frac{2 \sin{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \cos{\left(3 x \right)}}\right) \cos^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 2 3 2 \
asin(3*x) | / log(cos(3*x)) asin(3*x)*sin(3*x)\ 3 log(cos(3*x)) / log(cos(3*x)) asin(3*x)*sin(3*x)\ |sin (3*x)*asin(3*x) 3*x*log(cos(3*x)) 2*sin(3*x) | 3*sin (3*x) 2*asin(3*x)*sin(3*x) 2*sin (3*x)*asin(3*x) 27*x *log(cos(3*x)) 9*x*sin(3*x) |
27*cos (3*x)*|- |- ------------- + ------------------| - ------------- + ------------- + 3*|- ------------- + ------------------|*|------------------- - ----------------- + ---------------------- + asin(3*x)| - ----------------------- - -------------------- - --------------------- + ------------------- - ----------------------|
| | __________ cos(3*x) | __________ 3/2 | __________ cos(3*x) | | 2 3/2 __________ | __________ cos(3*x) 3 5/2 3/2 |
| | / 2 | / 2 / 2\ | / 2 | | cos (3*x) / 2\ / 2 | / 2 2 cos (3*x) / 2\ / 2\ |
\ \ \/ 1 - 9*x / \/ 1 - 9*x \1 - 9*x / \ \/ 1 - 9*x / \ \1 - 9*x / \/ 1 - 9*x *cos(3*x) / \/ 1 - 9*x *cos (3*x) \1 - 9*x / \1 - 9*x / *cos(3*x)/
$$27 \left(\frac{27 x^{2} \log{\left(\cos{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} - \frac{9 x \sin{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \cos{\left(3 x \right)}} - \left(\frac{\sin{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \frac{\log{\left(\cos{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right)^{3} + 3 \left(\frac{\sin{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \frac{\log{\left(\cos{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right) \left(- \frac{3 x \log{\left(\cos{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{\sin^{2}{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} + \operatorname{asin}{\left(3 x \right)} + \frac{2 \sin{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \cos{\left(3 x \right)}}\right) - \frac{2 \sin^{3}{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos^{3}{\left(3 x \right)}} - \frac{2 \sin{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \frac{3 \sin^{2}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \cos^{2}{\left(3 x \right)}} - \frac{3}{\sqrt{1 - 9 x^{2}}} + \frac{\log{\left(\cos{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right) \cos^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}$$
Gráfico