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^4/3-x
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Derivada de x^-4/5
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Derivada de x=1
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Derivada de x^2*2^x
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Expresiones idénticas
- y=(sin^2x)^ln^2x
- y es igual a ( seno de al cuadrado x) en el grado ln al cuadrado x
- y=(sin2x)ln2x
- y=sin2xln2x
- y=(sin²x)^ln²x
- y=(sin en el grado 2x) en el grado ln en el grado 2x
- y=sin^2x^ln^2x
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Expresiones con funciones
- Seno sin
- sin(x+π)
- sin(7*x)^(2)
- sin(3*y)
- sin(2*x-pi/3)
- sin^-1(cosx)
Derivada de y=(sin^2x)^ln^2x
Solución
Ha introducido
[src]
2
log (x)
2
sin (x)
$$\left(\sin^{2}{\left(x \right)}\right)^{\log{\left(x \right)}^{2}}$$
(sin(x)^2)^(log(x)^2)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
2 / / 2 \ 2 \
2*log (x) |2*log(x)*log\sin (x)/ 2*log (x)*cos(x)|
|sin(x)| *|--------------------- + ----------------|
\ x sin(x) /
$$\left(\frac{2 \log{\left(x \right)}^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \log{\left(x \right)} \log{\left(\sin^{2}{\left(x \right)} \right)}}{x}\right) \left|{\sin{\left(x \right)}}\right|^{2 \log{\left(x \right)}^{2}}$$
Segunda derivada
[src]
2 / / 2 \ / 2 \ 2 2 / / 2 \ \ \
2*log (x) | 2 log\sin (x)/ log(x)*log\sin (x)/ cos (x)*log (x) 2 |log\sin (x)/ cos(x)*log(x)| /2*log(|sin(x)|) cos(x)*log(x)*sign(sin(x))\ 4*cos(x)*log(x)|
2*|sin(x)| *|- log (x) + ------------ - ------------------- - --------------- + 2*log (x)*|------------ + -------------|*|--------------- + --------------------------| + ---------------|
| 2 2 2 \ x sin(x) / \ x |sin(x)| / x*sin(x) |
\ x x sin (x) /
$$2 \left(2 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin^{2}{\left(x \right)} \right)}}{x}\right) \left(\frac{\log{\left(x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|} + \frac{2 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{x}\right) \log{\left(x \right)}^{2} - \log{\left(x \right)}^{2} - \frac{\log{\left(x \right)}^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{4 \log{\left(x \right)} \cos{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{\log{\left(x \right)} \log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{2}} + \frac{\log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{2}}\right) \left|{\sin{\left(x \right)}}\right|^{2 \log{\left(x \right)}^{2}}$$
Tercera derivada
[src]
2 / / 2 \ / / 2 \ / 2 \ 2 2 \ / / 2 \ \ / 2 2 2 2 2 2 \ / 2 \ 3 2 2 2 / / 2 \ \ 2 \
2*log (x) | 6*log(x) 3*log\sin (x)/ /2*log(|sin(x)|) cos(x)*log(x)*sign(sin(x))\ | 2 log\sin (x)/ log(x)*log\sin (x)/ cos (x)*log (x) 4*cos(x)*log(x)| |log\sin (x)/ cos(x)*log(x)| | 2*log(|sin(x)|) 2*log(x)*log(|sin(x)|) log (x)*sign(sin(x))*sin(x) cos (x)*log (x)*sign (sin(x)) 2*cos (x)*log (x)*DiracDelta(sin(x)) 4*cos(x)*log(x)*sign(sin(x))| 2*log(x)*log\sin (x)/ 2*cos (x)*log (x) 2*log (x)*cos(x) /2*log(|sin(x)|) cos(x)*log(x)*sign(sin(x))\ 3 |log\sin (x)/ cos(x)*log(x)| 6*cos(x) 6*cos (x)*log(x) 6*cos(x)*log(x)|
2*|sin(x)| *|- -------- - -------------- - 4*|--------------- + --------------------------|*|log (x) - ------------ + ------------------- + --------------- - ---------------|*log(x) - 2*|------------ + -------------|*|- --------------- + ---------------------- + --------------------------- + ----------------------------- - ------------------------------------ - ----------------------------|*log(x) + --------------------- + ----------------- + ---------------- + 4*|--------------- + --------------------------| *log (x)*|------------ + -------------| + --------- - ---------------- - ---------------|
| x 3 \ x |sin(x)| / | 2 2 2 x*sin(x) | \ x sin(x) / | 2 2 |sin(x)| 2 |sin(x)| x*|sin(x)| | 3 3 sin(x) \ x |sin(x)| / \ x sin(x) / 2 2 2 |
\ x \ x x sin (x) / \ x x sin (x) / x sin (x) x *sin(x) x*sin (x) x *sin(x) /
$$2 \left(4 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin^{2}{\left(x \right)} \right)}}{x}\right) \left(\frac{\log{\left(x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|} + \frac{2 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{x}\right)^{2} \log{\left(x \right)}^{3} - 2 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\log{\left(\sin^{2}{\left(x \right)} \right)}}{x}\right) \left(\frac{\log{\left(x \right)}^{2} \sin{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|} - \frac{2 \log{\left(x \right)}^{2} \cos^{2}{\left(x \right)} \delta\left(\sin{\left(x \right)}\right)}{\left|{\sin{\left(x \right)}}\right|} + \frac{\log{\left(x \right)}^{2} \cos^{2}{\left(x \right)} \operatorname{sign}^{2}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 \log{\left(x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{x \left|{\sin{\left(x \right)}}\right|} + \frac{2 \log{\left(x \right)} \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{x^{2}} - \frac{2 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{x^{2}}\right) \log{\left(x \right)} - 4 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|} + \frac{2 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)}}{x}\right) \left(\log{\left(x \right)}^{2} + \frac{\log{\left(x \right)}^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 \log{\left(x \right)} \cos{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{\log{\left(x \right)} \log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{2}} - \frac{\log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{2}}\right) \log{\left(x \right)} + \frac{2 \log{\left(x \right)}^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \log{\left(x \right)}^{2} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{6 \log{\left(x \right)}}{x} - \frac{6 \log{\left(x \right)} \cos^{2}{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{6 \log{\left(x \right)} \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{6 \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2 \log{\left(x \right)} \log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{3}} - \frac{3 \log{\left(\sin^{2}{\left(x \right)} \right)}}{x^{3}}\right) \left|{\sin{\left(x \right)}}\right|^{2 \log{\left(x \right)}^{2}}$$