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:
- Derivada de i*n*x
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Derivada de y=6x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de 2^-x
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Expresiones idénticas
- y=sqrt(x)^((sin^ dos)x)
- y es igual a raíz cuadrada de (x) en el grado (( seno de al cuadrado )x)
- y es igual a raíz cuadrada de (x) en el grado (( seno de en el grado dos)x)
- y=√(x)^((sin^2)x)
- y=sqrt(x)((sin2)x)
- y=sqrtxsin2x
- y=sqrt(x)^((sin²)x)
- y=sqrt(x) en el grado ((sin en el grado 2)x)
- y=sqrtx^sin^2x
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x)+1/x
- sqrt(x)+1/(sqrt(x))
- sqrt(x/(x+1))
- sqrt(x^2-8*x+17)
- sqrt(x+1)/x^3
- Seno sin
- sin(x)/cos(x)^(2)
- sin(x)^(5)
- sin(x)^(4)
- sin(x)^(x^2)
- sin(x)*sin(x)*sin(x)
Derivada de y=sqrt(x)^((sin^2)x)
Solución
Ha introducido
[src]
2
sin (x)*x
___
\/ x
$$\left(\sqrt{x}\right)^{x \sin^{2}{\left(x \right)}}$$
(sqrt(x))^(sin(x)^2*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
Primera derivada
[src]
2
x*sin (x)
--------- / 2 \
2 |sin (x) / 2 \ / ___\|
x *|------- + \sin (x) + 2*x*cos(x)*sin(x)/*log\\/ x /|
\ 2 /
$$x^{\frac{x \sin^{2}{\left(x \right)}}{2}} \left(\left(2 x \sin{\left(x \right)} \cos{\left(x \right)} + \sin^{2}{\left(x \right)}\right) \log{\left(\sqrt{x} \right)} + \frac{\sin^{2}{\left(x \right)}}{2}\right)$$
Segunda derivada
[src]
2
x*sin (x)
--------- / 2 / / ___\ \\
2 | / 2 2 \ / ___\ (2*x*cos(x) + sin(x))*sin(x) sin (x)*((2*x*cos(x) + sin(x))*log(x) + sin(x))*\2*(2*x*cos(x) + sin(x))*log\\/ x / + sin(x)/|
x *|cos(x)*sin(x) + 2*\x*cos (x) - x*sin (x) + 2*cos(x)*sin(x)/*log\\/ x / + ---------------------------- + ---------------------------------------------------------------------------------------------|
\ 2*x 4 /
$$x^{\frac{x \sin^{2}{\left(x \right)}}{2}} \left(\frac{\left(2 \left(2 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sqrt{x} \right)} + \sin{\left(x \right)}\right) \left(\left(2 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} + \sin{\left(x \right)}\right) \sin^{2}{\left(x \right)}}{4} + 2 \left(- x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \log{\left(\sqrt{x} \right)} + \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\left(2 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \sin{\left(x \right)}}{2 x}\right)$$
Tercera derivada
[src]
2
x*sin (x) / / / 2 2 \ / ___\ (2*x*cos(x) + sin(x))*sin(x)\ / / ___\ \ / / 2 2 \ (2*x*cos(x) + sin(x))*sin(x)\ \
--------- | / 2 2 \ ((2*x*cos(x) + sin(x))*log(x) + sin(x))*|2*cos(x)*sin(x) + 4*\x*cos (x) - x*sin (x) + 2*cos(x)*sin(x)/*log\\/ x / + ----------------------------|*sin(x) \2*(2*x*cos(x) + sin(x))*log\\/ x / + sin(x)/*|2*\x*cos (x) - x*sin (x) + 2*cos(x)*sin(x)/*log(x) + 2*cos(x)*sin(x) + ----------------------------|*sin(x) 2 3 / / ___\ \|
2 | 2 2 / 2 2 \ / ___\ 2*\x*cos (x) - x*sin (x) + 2*cos(x)*sin(x)/ \ x / (2*x*cos(x) + sin(x))*sin(x) \ x / ((2*x*cos(x) + sin(x))*log(x) + sin(x)) *sin (x)*\2*(2*x*cos(x) + sin(x))*log\\/ x / + sin(x)/|
x *|cos (x) - sin (x) - 2*\- 3*cos (x) + 3*sin (x) + 4*x*cos(x)*sin(x)/*log\\/ x / + ------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------|
| x 2 2 4 8 |
\ 2*x /
$$x^{\frac{x \sin^{2}{\left(x \right)}}{2}} \left(\frac{\left(2 \left(2 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sqrt{x} \right)} + \sin{\left(x \right)}\right) \left(\left(2 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} + \sin{\left(x \right)}\right)^{2} \sin^{3}{\left(x \right)}}{8} + \frac{\left(2 \left(2 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(\sqrt{x} \right)} + \sin{\left(x \right)}\right) \left(2 \left(- x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \log{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\left(2 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \sin{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{4} + \frac{\left(\left(2 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} + \sin{\left(x \right)}\right) \left(4 \left(- x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \log{\left(\sqrt{x} \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)} + \frac{\left(2 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \sin{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{2} - 2 \left(4 x \sin{\left(x \right)} \cos{\left(x \right)} + 3 \sin^{2}{\left(x \right)} - 3 \cos^{2}{\left(x \right)}\right) \log{\left(\sqrt{x} \right)} - \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} + \frac{2 \left(- x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{x} - \frac{\left(2 x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \sin{\left(x \right)}}{2 x^{2}}\right)$$
Gráfico