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=((3x^ dos)- uno)^lnsinx
- y es igual a ((3x al cuadrado ) menos 1) en el grado ln seno de x
- y es igual a ((3x en el grado dos) menos uno) en el grado ln seno de x
- y=((3x2)-1)lnsinx
- y=3x2-1lnsinx
- y=((3x²)-1)^lnsinx
- y=((3x en el grado 2)-1) en el grado lnsinx
- y=3x^2-1^lnsinx
-
Expresiones semejantes
- y=((3x^2)+1)^lnsinx
Derivada de y=((3x^2)-1)^lnsinx
Solución
Ha introducido
[src]
log(sin(x)) / 2 \ \3*x - 1/
$$\left(3 x^{2} - 1\right)^{\log{\left(\sin{\left(x \right)} \right)}}$$
(3*x^2 - 1)^log(sin(x))
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
log(sin(x)) / / 2 \ \
/ 2 \ |cos(x)*log\3*x - 1/ 6*x*log(sin(x))|
\3*x - 1/ *|-------------------- + ---------------|
| sin(x) 2 |
\ 3*x - 1 /
$$\left(3 x^{2} - 1\right)^{\log{\left(\sin{\left(x \right)} \right)}} \left(\frac{6 x \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1} + \frac{\log{\left(3 x^{2} - 1 \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)$$
Segunda derivada
[src]
/ 2 \
log(sin(x)) |/ / 2\ \ 2 / 2\ 2 |
/ 2\ ||cos(x)*log\-1 + 3*x / 6*x*log(sin(x))| / 2\ 6*log(sin(x)) cos (x)*log\-1 + 3*x / 36*x *log(sin(x)) 12*x*cos(x) |
\-1 + 3*x / *||--------------------- + ---------------| - log\-1 + 3*x / + ------------- - ---------------------- - ----------------- + ------------------|
|| sin(x) 2 | 2 2 2 / 2\ |
|\ -1 + 3*x / -1 + 3*x sin (x) / 2\ \-1 + 3*x /*sin(x)|
\ \-1 + 3*x / /
$$\left(3 x^{2} - 1\right)^{\log{\left(\sin{\left(x \right)} \right)}} \left(- \frac{36 x^{2} \log{\left(\sin{\left(x \right)} \right)}}{\left(3 x^{2} - 1\right)^{2}} + \frac{12 x \cos{\left(x \right)}}{\left(3 x^{2} - 1\right) \sin{\left(x \right)}} + \left(\frac{6 x \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1} + \frac{\log{\left(3 x^{2} - 1 \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} - \log{\left(3 x^{2} - 1 \right)} - \frac{\log{\left(3 x^{2} - 1 \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{6 \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1}\right)$$
Tercera derivada
[src]
/ 3 \
log(sin(x)) |/ / 2\ \ / / 2\ \ / 2 / 2\ 2 \ 3 / 2\ / 2\ 3 2 2 |
/ 2\ ||cos(x)*log\-1 + 3*x / 6*x*log(sin(x))| 18*x |cos(x)*log\-1 + 3*x / 6*x*log(sin(x))| | 6*log(sin(x)) cos (x)*log\-1 + 3*x / 36*x *log(sin(x)) 12*x*cos(x) / 2\| 108*x*log(sin(x)) 2*cos (x)*log\-1 + 3*x / 2*cos(x)*log\-1 + 3*x / 18*cos(x) 432*x *log(sin(x)) 108*x *cos(x) 18*x*cos (x) |
\-1 + 3*x / *||--------------------- + ---------------| - --------- - 3*|--------------------- + ---------------|*|- ------------- + ---------------------- + ----------------- - ------------------ + log\-1 + 3*x /| - ----------------- + ------------------------ + ----------------------- + ------------------ + ------------------ - ------------------- - -------------------|
|| sin(x) 2 | 2 | sin(x) 2 | | 2 2 2 / 2\ | 2 3 sin(x) / 2\ 3 2 / 2\ 2 |
|\ -1 + 3*x / -1 + 3*x \ -1 + 3*x / | -1 + 3*x sin (x) / 2\ \-1 + 3*x /*sin(x) | / 2\ sin (x) \-1 + 3*x /*sin(x) / 2\ / 2\ \-1 + 3*x /*sin (x)|
\ \ \-1 + 3*x / / \-1 + 3*x / \-1 + 3*x / \-1 + 3*x / *sin(x) /
$$\left(3 x^{2} - 1\right)^{\log{\left(\sin{\left(x \right)} \right)}} \left(\frac{432 x^{3} \log{\left(\sin{\left(x \right)} \right)}}{\left(3 x^{2} - 1\right)^{3}} - \frac{108 x^{2} \cos{\left(x \right)}}{\left(3 x^{2} - 1\right)^{2} \sin{\left(x \right)}} - \frac{18 x}{3 x^{2} - 1} - \frac{18 x \cos^{2}{\left(x \right)}}{\left(3 x^{2} - 1\right) \sin^{2}{\left(x \right)}} - \frac{108 x \log{\left(\sin{\left(x \right)} \right)}}{\left(3 x^{2} - 1\right)^{2}} + \left(\frac{6 x \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1} + \frac{\log{\left(3 x^{2} - 1 \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} - 3 \left(\frac{6 x \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1} + \frac{\log{\left(3 x^{2} - 1 \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\frac{36 x^{2} \log{\left(\sin{\left(x \right)} \right)}}{\left(3 x^{2} - 1\right)^{2}} - \frac{12 x \cos{\left(x \right)}}{\left(3 x^{2} - 1\right) \sin{\left(x \right)}} + \log{\left(3 x^{2} - 1 \right)} + \frac{\log{\left(3 x^{2} - 1 \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{6 \log{\left(\sin{\left(x \right)} \right)}}{3 x^{2} - 1}\right) + \frac{2 \log{\left(3 x^{2} - 1 \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \log{\left(3 x^{2} - 1 \right)} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{18 \cos{\left(x \right)}}{\left(3 x^{2} - 1\right) \sin{\left(x \right)}}\right)$$
Gráfico