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/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- y=√x^(sin2x)
- y es igual a √x en el grado ( seno de 2x)
- y=√x(sin2x)
- y=√xsin2x
- y=√x^sin2x
Derivada de y=√x^(sin2x)
Solución
Ha introducido
[src]
sin(2*x) ___ \/ x
$$\left(\sqrt{x}\right)^{\sin{\left(2 x \right)}}$$
(sqrt(x))^sin(2*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
sin(2*x)
--------
2 /sin(2*x) / ___\\
x *|-------- + 2*cos(2*x)*log\\/ x /|
\ 2*x /
$$x^{\frac{\sin{\left(2 x \right)}}{2}} \left(2 \log{\left(\sqrt{x} \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{2 x}\right)$$
Segunda derivada
[src]
sin(2*x) / /sin(2*x) \ /sin(2*x) / ___\\\
-------- | |-------- + 2*cos(2*x)*log(x)|*|-------- + 4*cos(2*x)*log\\/ x /||
2 | / ___\ 2*cos(2*x) sin(2*x) \ x / \ x /|
x *|- 4*log\\/ x /*sin(2*x) + ---------- - -------- + -----------------------------------------------------------------|
| x 2 4 |
\ 2*x /
$$x^{\frac{\sin{\left(2 x \right)}}{2}} \left(\frac{\left(4 \log{\left(\sqrt{x} \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right) \left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right)}{4} - 4 \log{\left(\sqrt{x} \right)} \sin{\left(2 x \right)} + \frac{2 \cos{\left(2 x \right)}}{x} - \frac{\sin{\left(2 x \right)}}{2 x^{2}}\right)$$
Tercera derivada
[src]
/ /sin(2*x) \ /sin(2*x) 4*cos(2*x) / ___\ \ /sin(2*x) / ___\\ /sin(2*x) 4*cos(2*x) \ 2 \
sin(2*x) | |-------- + 2*cos(2*x)*log(x)|*|-------- - ---------- + 8*log\\/ x /*sin(2*x)| |-------- + 4*cos(2*x)*log\\/ x /|*|-------- - ---------- + 4*log(x)*sin(2*x)| /sin(2*x) \ /sin(2*x) / ___\\|
-------- | \ x / | 2 x | \ x / | 2 x | |-------- + 2*cos(2*x)*log(x)| *|-------- + 4*cos(2*x)*log\\/ x /||
2 |sin(2*x) / ___\ 6*sin(2*x) 3*cos(2*x) \ x / \ x / \ x / \ x /|
x *|-------- - 8*cos(2*x)*log\\/ x / - ---------- - ---------- - ------------------------------------------------------------------------------ - ------------------------------------------------------------------------------ + ------------------------------------------------------------------|
| 3 x 2 2 4 8 |
\ x x /
$$x^{\frac{\sin{\left(2 x \right)}}{2}} \left(\frac{\left(4 \log{\left(\sqrt{x} \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right) \left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right)^{2}}{8} - \frac{\left(4 \log{\left(\sqrt{x} \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right) \left(4 \log{\left(x \right)} \sin{\left(2 x \right)} - \frac{4 \cos{\left(2 x \right)}}{x} + \frac{\sin{\left(2 x \right)}}{x^{2}}\right)}{4} - \frac{\left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right) \left(8 \log{\left(\sqrt{x} \right)} \sin{\left(2 x \right)} - \frac{4 \cos{\left(2 x \right)}}{x} + \frac{\sin{\left(2 x \right)}}{x^{2}}\right)}{2} - 8 \log{\left(\sqrt{x} \right)} \cos{\left(2 x \right)} - \frac{6 \sin{\left(2 x \right)}}{x} - \frac{3 \cos{\left(2 x \right)}}{x^{2}} + \frac{\sin{\left(2 x \right)}}{x^{3}}\right)$$
Gráfico